Improving credit risk assessment in P2P lending with explainable machine learning survival analysis

Bone-Winkel, Ge o F ied ich; Reichenbach, Felix
A icle — Published Ve sion
Imp o ing c edi isk assessmen in P2P lending wi h
explainable machine lea ning su i al analysis
Digi al Finance
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Bone-Winkel, Ge o F ied ich; Reichenbach, Felix (2024) : Imp o ing c edi isk
assessmen in P2P lending wi h explainable machine lea ning su i al analysis, Digi al Finance,
ISSN 2524-6186, Sp inge In e na ional Publishing, Cham, Vol. 6, Iss. 3, pp. 501-542,
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Digi al Finance (2024) 6:501–542
h ps://doi.o g/10.1007/s42521-024-00114-3
1 3
ORIGINAL ARTICLE
Imp o ing c edi isk assessmen inP2P lending
wi hexplainable machine lea ning su i al analysis
Ge oF ied ichBone‑Winkel1· FelixReichenbach2
Recei ed: 4 Ma ch 2024 / Accep ed: 17 May 2024 / Published online: 12 June 2024
© The Au ho (s) 2024
Abs ac
Recen esea ch using explainable machine lea ning su i al analysis demons a ed
i s abili y o iden i y new isk ac o s in he medical ield. In his s udy, we adap ed
his me hodology o c edi isk assessmen . We used a comp ehensi e da ase om
he Es onian P2P lending pla o m Bondo a, consis ing o o e 350,000 loans and
112 ea u es wi h a loan olume o 915million eu os. Fi s , we applied classical
(linea ) and machine lea ning (ex eme g adien -boos ed) Cox models o es ima e
he isk o hese loans and hen isk- a ed hem using isk s a i ica ion. Fo each
a ing ca ego y we calcula ed de aul a es, a es o e u n, and plo ed Kaplan–
Meie cu es. These pe o mance c i e ia e ealed ha he boos ed Cox model
ou pe o med bo h he classical Cox model and he pla o m’s a ing. Fo ins ance,
he boos ed model’s highes a ing ca ego y had an annual excess e u n o 18% and
a lowe de aul a e compa ed o he pla o m’s bes a ing. Second, we explained
he machine lea ning model’s ou pu using Shapley Addi i e Explana ions. This
analysis e ealed no el nonlinea ela ionships (e.g., highe isk o bo owe s
o e age 55) and in e ac ion e ec s (e.g., be ween age and housing si ua ion) ha
p o ide p omising a enues o u u e esea ch. The machine-lea ning model also
ound ea u e con ibu ions aligning wi h exis ing esea ch, such as lowe de aul
isk associa ed wi h olde bo owe s, emales, indi iduals wi h mo gages, o hose
wi h highe educa ion. O e all, ou esul s e eal ha explainable machine lea ning
su i al analysis excels a isk a ing, p o i sco ing, and isk ac o analysis,
acili a ing mo e p ecise and anspa en c edi isk assessmen s.
Keywo ds P2P lending· Explainable AI· Cox model· C edi isk· SHAP· Su i al
analysis
JEL Classi ica ion G10· G21· G32· G33· G51
* Felix Reichenbach
. eichenbac[email p o ec ed]
1 Technische Uni e si ä Be lin, S aße des 17. Juni 135, 16023Be lin, Ge many
2 Chai o Finance andIn es men , Technische Uni e si ä Be lin, S aße des 17. Juni 135,
10623Be lin, Ge many
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Digi al Finance (2024) 6:501–542
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1 In oduc ion
D i en by echnological ad ancemen s, Pee - o-Pee (P2P) lending mee s a
g owing demand o al e na i e inancing and pe sonal loans (Su yono e al., 2019).
These loans a e ypically unsecu ed (De Rou e e al., 2016) and lende s bea he
isk o de aul . Mos majo P2P lending pla o ms se in e es a es based on hei
in e nal a ing models. On hese pla o ms, accu a e isk assessmen is c ucial: I
he pla o m o e es ima es he isk o a loan, he bo owe migh be able o ge a
cheape loan elsewhe e. I he isk is unde es ima ed, lende s migh no be able o
eco e hei in es men in case o de aul and migh no in es ia he pla o m
again. Howe e , he lack o c edi his o y and colla e al makes i di icul o assess
he c edi wo hiness o bo owe s using adi ional c edi isk assessmen me hods
(Ba oso, 2020).
Machine Lea ning (ML) is a p omising echnology ha could p o e key o
mo e accu a e isk e alua ion (Zhang e al., 2015). While many s udies ha e been
conduc ed on he opic o c edi isk assessmen using ML, mos ocus on p edic ing
bina y de aul , a he han de aul iming. Mo eo e , ML is o en seen as a “black
box”—powe ul a isk-classi ica ion, bu no well sui ed o analyzing he economic
impac o indi idual isk ac o s. Acco dingly, his (pe cei ed) ade-o be ween
explana o y and p edic i e pe o mance limi s he use ulness o ML me hods in isk
managemen (Van Liebe gen, 2017). Howe e , ecen de elopmen s in explainable
ML demons a e ha he wo a e no necessa ily a odds, wi h ML su i al analysis
me hods iden i ying bo h known and no el isk ac o s o b eas cance su i al
(Liu e al., 2023; Moncada-To es e al., 2021).
Ou s udy applies his p omising me hodology o c edi isk assessmen in P2P
lending. We use a da ase om he Es onian pla o m Bondo a consis ing o o e
350,000 loans and 112 ea u es wi h a olume o €915 million a he end o 2023.
Using classical and ex eme g adien -boos ed Cox models, we p edic he isk o
P2P loans. Subsequen ly, we assign isk a ings using isk s a i ica ion. We show
ha he a ings based on he ML model (i.e., he boos ed Cox model) signi ican ly
ou pe o m bo h Bondo a’s isk a ing and he a ing based on he classical model
(i.e., he linea Cox model).1 We also discuss he p ac ical implica ions o isk
sc eening, se ing ai e in e es a es and he po en ial p o i oppo uni ies o
in es o s when using hese models.
Then, we open he “black box” o ML by using Shapley Addi i e Explana ions
(SHAP) o explain and compa e he models (Lundbe g & Lee, 2017). He e, we
examine he di e ences be ween he classical and ML Cox model and e alua e
how he ML model can be used o iden i y isk ac o s in P2P lending. Ou analysis
unco e s isk ac o s ha align wi h hose iden i ied in p io s udies, while also
un eiling no el ela ionships wi h nonlinea and in e ac ion e ec s.
1 While i could be a gued ha “classical” (linea ) Cox models a e also a o m o ML, we ollow Ley
e al. (2022) in dis inguishing be ween he wo: Classical models a e de ined by he use ( op-down),
whe eas ML models a e de ined by he algo i hm (bo om-up and d i en by he da a). AppendixB p o-
ides a mo e de ailed discussion o his issue.
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Digi al Finance (2024) 6:501–542
In summa y, we demons a e ha wi h supe io p edic i e and explana o y pe -
o mance, explainable ML su i al analysis is no only a use ul ool o c edi sco -
ing bu also o he examina ion o c edi isk ac o s. The s udy is s uc u ed as ol-
lows. Sec ion2 p esen s he heo y, e iews he exis ing esea ch on isk assessmen
me hodologies, and ou lines he con ibu ion and objec i es o ou s udy. Sec ion3
hen in oduces he da ase s and ou me hodical app oach.2 Sec ion4 p esen s he
model’s pe o mance and explana ions, which we in e p e and discuss in Sec .5,
ollowed by Sec .6 ha concludes he s udy.
2 Theo e ical backg ound andli e a u e
In he ollowing subsec ions, we b ie ly e iew he li e a u e on c edi isk modeling
in P2P lending and explainable ML. Fu he mo e, we iden i y he esea ch gap and
discuss he objec i es and con ibu ion o his s udy.
2.1 C edi isk modeling inP2P lending
As ou lined in he in oduc ion, accu a e isk assessmen is essen ial o pla o ms,
bo owe s, and lende s. Howe e , a e iew by Su yono e al. (2019) unde sco es ha
isk assessmen poses a majo challenge in P2P lending due o la ge in o ma ion
asymme y, lack o c edi his o y, gende disc imina ion, and low loan success a es.
The e iew u he iden i ies ML me hods and big da a as po en ial solu ions o
hese issues.
In es iga ing c edi isk is a well-es ablished ield o esea ch and has been
s udied ex ensi ely using bina y classi ica ion. Bina y classi ica ion aims o
p edic whe he a bo owe will de aul . I has been s udied widely on P2P lending
da ase s using s a is ical (e.g., Emek e e al., 2015; Se ano-Cinca e  al., 2015),
ML (e.g., Jiang e al., 2018; Xu e al., 2021; Zhou e al., 2019), and a ely using
explainable ML me hods (e.g., A iza-Ga zón e al., 2020; Bussmann e al., 2021).
In p ac ice, like mos s udies, banks ypically use bina y classi ica ion o calcula e
he p obabili y o de aul o c edi sco ing (Dömö ö e al., 2023). While hei exac
me hod is no disclosed, Bondo a’s a ings a e based on expec ed loss, which also
akes in o accoun he likelihood o eco e y a e de aul (Bondo a, 2023c).3
Su i al analysis o e s an al e na i e app oach ha has some ad an ages o e
adi ional classi ica ion me hods: Fi s , su i al analysis akes in o accoun he ime
du a ion un il a loan de aul s. This is no done when analyzing he de aul s a us
alone. Howe e , ime o de aul plays a c ucial ole in e u n on in es men and
2 AppendixB o e s a mo e de ailed exposi ion o he models, pe o mance me ics, isk a ing, and
explainable ML, se ing as an accessible guide o p ac i ione s and esea che s keen on applying his
inno a i e me hodology.
3 These a ings a e based in pa on sensi i e da a ha lende s legally canno access. This includes p io
loan applica ions, and in o ma ion om c edi bu eaus, popula ion egis ies, banks, and ax au ho i-
ies (Bondo a, 2023c). By encoding in o ma ion una ailable o lende s in a ings, Bondo a could educe
unce ain y be ween lende s and bo owe s. Howe e , i he a ings do no accu a ely e lec a loan’s isk
p o ile, i can lead o misp icing h ough oo high o oo low in e es a es.
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expec ed loss: Wi h la e de aul s, he exposu e a de aul and hus in es men a
isk is lowe . This is pa icula ly impo an in he case o ixed- a e loans, whe e he
ou s anding paymen s o in es o s a e much highe when he loan de aul s on he
i s paymen as opposed o he las paymen . Second, su i al analysis also enables
including loans in he aining da ase ha ha e no ye eached ma u i y h ough
censo ing. This can be a signi ican ad an age, especially o long ma u i ies, as i
allows o he use o mo e ecen da a. A hi d ad an age is ha esea che s can use
su i al unc ions o examine he in luence o cha ac e is ics on sol ency o e ime,
which may p o ide insigh s in o possible unde lying causes. This is p omising in
p ac ice, e.g., when e alua ing loans in seconda y ma ke s, bo owe cha ac e is ics
may ha e a di e en e ec a e a ce ain pe iod o ime.
While s a is ical su i al analysis models like linea Cox eg ession a e used in
some s udies on P2P lending da ase s (e.g., Emek e e al., 2015; Se ano-Cinca
e al., 2015), ew ML-based su i al analysis s udies exis (Suá ez-Ramí ez e al.,
2022; Tan e al., 2019) and none o hese use explainable ML me hods. Ne e heless,
when p oposing a no el ML su i al-analysis me hod (Bai e al., 2022) demons a e
ha ML-based su i al analysis can ou pe o m s a is ical su i al analysis me hods
in de aul classi ica ion.
2.2 Explainable machine lea ning andcon ibu ion
The sca ci y o ML su i al analysis s udies in ecen li e a u e may be caused by
seemingly con lic ing goals o hei me hodologies: While popula su i al analysis
me hods like linea Cox eg ession a e commonly used o hei in e p e abili y
in isk ac o assessmen (Emek e e  al., 2015; Reichenbach & Wal he , 2021;
Se ano-Cinca e al., 2015), ML me hods ocus on p edic i e accu acy and a e mo e
di icul o in e p e . E en he mos p ecise p edic ions om a ML Cox model may
no be e y use ul i hey a e no in e p e able.
Recen esea ch add esses his issue wi h he model agnos ic and scalable
explainable ML me hod SHAP (Lundbe g and Lee, 2017; Lundbe g e al., 2019,
2020; Mi chell e  al., 2022). This me hod enables he explainabili y o ML Cox
models, un eiling much mo e complex nonlinea ela ionships and in e ac ion
e ec s han he linea models could cap u e. This combina ion o me hods yielded
b eak h ough esul s in clinical esea ch, iden i ying bo h clinically con i med
and po en ially no el isk indica o s o b eas cance su i al (Liu e  al., 2023;
Moncada-To es e al., 2021) using explainable ML su i al analysis.
To he bes o ou knowledge, explainable ML su i al analysis has no ye been
applied o P2P lending. This s udy aims o add ess his esea ch gap by p esen ing
explainable ML-based su i al analysis as a use ul ool o bo h c edi sco ing (i.e.,
classi ica ion using isk a ings) and he (in e en ial) analysis o di e en isk ac o s
(e.g., deb - o-income, age, educa ion) in P2P lending. Thus, we seek o con ibu e
o bo h he li e a u e on c edi sco ing echniques and he analysis o isk ac o s o
indi idual bo owe s.

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Digi al Finance (2024) 6:501–542
Conce ning he Bondo a da ase used o es he me hods, p e ious s udies ound
oom o imp o emen in c edi isk sco ing (e.g., Dömö ö e al., 2023; Lyócsa
e al., 2022; Teply & Polena, 2020), and signs o asse misp icing on he seconda y
ma ke (Caglayan e al., 2020). Howe e , as discussed abo e, he da a has no been
ex ensi ely s udied using in e p e able ML and su i al analysis me hods.
3 Da a andme hods
In his sec ion, we b ie ly p esen he da a and me hods used in his s udy.
Fo eade s no amilia wi h su i al analysis, ML, o SHAP, we ecommend
eading ou mo e de ailed in oduc ion o hese me hods in Appendix B, whe e
we in oduce classical (Cox) models, hei p edic ions and how hese can be
gene alized using ML me hods. We also explain how SHAP alues a e used o
explain ML p edic ions.
The me hodology o ou s udy consis s o 6 majo s eps: (1) p ep ocessing,
(2) sampling, (3) aining o he models, (4) a ing assignmen , (5) pe o mance
measu emen and (6) analysis o isk ac o s. These a e illus a ed by Fig.1 and
a e discussed in he ollowing subsec ions a e he p esen a ion o he da ase s.
3.1 Da ase s
We use wo da ase s p o ided by Bondo a (2023a) o ou analysis. These a e
upda ed daily and we e las e ie ed on Janua y 3, 2024. The loan da ase
con ains da a on all loans o igina ed on he Bondo a pla o m, including o e
350,000 loans om Es onia, Finland, and Spain. I s 112 ea u es p o ide de ails
on he bo owe s’ demog aphics, inancials, and bo owing his o y, as well as
isk a ings calcula ed by Bondo a and in o ma ion on he loan e ms and ou -
come (see AppendixA o a ull able wi h Bondo a’s de ini ions). Wi h loans
anging om 2009 un il he end o 2023, he o al cash olume o all loans
sums up o 915 million Eu os. The loans in he da ase ha e a ying ma u i ies,
he mos common being 5 and 3yea s. Ou s udy ocuses on 3-yea -loans as
he du a ion is sho enough, in ligh o he limi ed da a imespan a ailable, o
allow o he spli ing o aining, alida ion, and es da a in a empo al o de .
The ixed loan du a ion ensu es compa abili y be ween bo owe s when analyz-
ing he isk ac o s using su i al analysis (see AppendixB.1). The ollowing
da a and plo s add ess his subse .
As seen in Fig. 2 he majo i y o loans we e o igina ed a e 2017. The
o e all isk s uc u e o he po olio appea s o ha e shi ed owa ds less
isky loans a e 2019. This may be explained by Bondo a’s shi o hands-o 4
in es men om 2016 o 2020 (Bondo a, 2016). The lowe amoun o loans
since 2020 may be due o he COVID-19 pandemic and a ocus on highe -
quali y lende s.
4 Today, Bondo a exclusi ely o e s in es men s in o a single pla o m-managed po olio a a ixed
annual a e o e u n.
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Digi al Finance (2024) 6:501–542
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In addi ion, we use Bondo a’s epaymen s da ase (Bondo a, 2023a), which
con ains all paymen s ecei ed by in es o s (o e 6.2million in o al) o calcu-
la e he loans’ in e nal a e o e u n (IRR). In con as o he e u n on in es -
men , he IRR akes in o accoun he ime o paymen and he e o e indica es
Fig. 1 O e iew o he main p ep ocessing, aining and e alua ion s eps
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Digi al Finance (2024) 6:501–542
he ac ual a e o e u n ealized by he in es o s. The esul s o his analysis a e
p esen ed in Sec .4.1.
3.2 P ep ocessing
As seen in Fig.1, we p ep ocessed he da a o model aining in 10 s eps. To achie e
be e compa abili y, we ain bo h models on he same da ase s. As such, hese s eps
ollow he s ic e equi emen s o he linea model by excluding missing alues.
Bene i ing he in e p e abili y o bo h models, we educe high dimensionali y,
co-dependencies and spa si y o he da a, leading o simple models and hus simple
SHAP explana ions.
Nex , we p esen he p ep ocessing s eps in mo e de ail: Fi s , we emo ed
37 ea u es no a ailable a he ime o he auc ion o a oid a ge leakage.5 This
includes da a abou he loan s a us, seconda y ma ke , and deb collec ion
p ocess. To iden i y hese ea u es, we consul ed he Bondo a auc ion Applica ion
P og amming In e ace (API) documen a ion (Bondo a, 2023b) and he Bondo a
websi e (Bondo a, 2023a). We hen emo ed ano he 16 ea u es no a ailable due
o da a p o ec ion laws a e June 1, 2017 (e.g., p i a e in o ma ion like ma i al
s a us and employmen posi ion, bu also inancials like deb - o-income (DTI)).
Fu he mo e o a oid o e i ing, we d opped ea u es no ele an o he analysis,
like he loan ID, loan numbe , use name, and ea u es abou he exac iming o he
lis ing like he paymen day, lis ing ime, weekday, and mon h.
As a ou h s ep, we modeled some ea u es ound ele an in p io li e a u e
ha a e no p esen in he da a and added con ol a iables: Deb ToIncomeMod-
eled measu es he a io be ween mon hly income and mon hly liabili ies plus loan
Fig. 2 Numbe o 3-yea -loans by o igina ion yea and isk a ing
5 Ta ge leakage occu s when da a no a ailable in he eal wo ld is used o ain a model (Kau man
e al., 2011).
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paymen s.6 Repaymen Ra io measu es he p e ious epaymen amoun s di ided by
he p e ious loan amoun s.7
Nex , we emo ed ea u es wi h a high pe cen age o missing alues: Da eO -
Bi h, Ci y, and Coun y we e missing o all bo owe s, likely because hey we e
e ac ed om he public da a. Addi ionally, we emo ed he coun y-speci ic c edi
sco es om ex e nal a ing agencies due o missing da a (be ween 41 and 91%). This
le us wi h a ew ea u es wi h less han 2% missing. Fo hese, we emo ed da a
poin s wi h any missing alues. This a ec ed 2.85% o he emaining bo owe s. Fo
ca ego ical ea u es, we emo ed unused and ex emely a e ca ego ies (less han
0.1% o he bo owe s), i.e., he only emaining homeless and 41 Slo akian bo ow-
e s. No e ha his s ep may in oduce bias o he bene i o imp o ed compa abili y
be ween he models and could be skipped o he boos ed model.
Then, we me ged he wo ca ego ies “income un e i ied” and “income un e i ied,
c oss- e e enced by phone” due o a e y low numbe o loans in he la e ca ego y
(less han 1%). As a signi ican po ion o Es onian bo owe s is Russian-speaking,
his popula ion was sepa a ed om he o he Es onian bo owe s as “EE_Ru”.
Fo o he coun y codes, he language spoken was mo e homogenous, and o he
languages we e oo a e o d aw any conclusions. A e ha , he ea u es “Language”
and “Coun y” we e emo ed om he da ase and eplaced by he new ea u e
“Coun y_Lang”.
We enamed ca ego ical ea u es encoded as numbe s (as seen in AppendixA)
o s ings o imp o e eadabili y in he plo s and emo e alse o dinali y. Addi ion-
ally, we enamed NewC edi Cus ome o NewBondo aCus ome , as his e lec s he
meaning o he ea u e be e , and co ec ed spelling mis akes. Fu he mo e, we use
one-ho encoding o he ca ego ical a iables when i ing he linea models. One-
ho encoding c ea es a new column o e e y ca ego ical alue (e.g., Ra ing_AA,
Ra ing_A
,…,
Ra ing_HR). The new columns con ain a 1 i he loan has he co e-
sponding a ing and a 0 o he wise. To a oid mul icollinea i y, we d opped he i s
ca ego y o each ea u e in hese models.
Finally, we added wo a iables needed o su i al analysis. Tha is he
su i al ime (Su i alTime) and an e en indica o (De aul ed). In ou analysis o
he Bondo a da ase , we de ine su i al ime and he de aul indica o as ollows.
Su i al ime is he ime in days be ween he loan o igina ion and he i s o he
ollowing e en s: de aul (de aul ed), end o he loan e m (no de aul ed), and end o
he obse a ion pe iod (no de aul ed), i.e., he spli da e o aining and alida ion
se s o he da e o he epo o he es ing se . In o he wo ds, we in es iga e how
long a subjec can obse ably mee he loan’s condi ions wi hou de aul . C ucially,
7 Howe e , some loans had no da a on p e ious epaymen s. This could be due o he loans being s ill
ac i e o he da a being una ailable. On op, some loans had no p e ious loans. Fo hese a iables, he
a io was no calculable and was se o 0. To con ol o his, we added a iables o unknown p e ious
epaymen s, namely NanEa lyRepaymen and NanRepaymen His o y.
6 Loan paymen s appea no o be included in Bondo a’s mon hly liabili ies a iable. This calcula ed
a io appea s o de ia e om he DTI a io calcula ed by Bondo a o da a p io o 2017. This de ia ion is
likely caused by he exclusion o some liabili ies and income sou ces om he da ase o da a p o ec ion
easons. Un o una ely, he exac calcula ion o he DTI a io, income, and liabili ies a e no disclosed by
Bondo a.
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ba s on he igh . The e ical dispe sion o he boos ed SHAP alues is explained
by ea u e in e ac ion e ec s. We will dissec hese o selec ed ea u es la e .
Figu es6 and7 show he SHAP alues o he boos ed and linea Cox model o
h ee selec ed ea u es om he demog aphics ca ego y, Coun y_Lang, Educa ion
Age. The ull dependence plo s o all 21 ea u es in he ca ego ies demog aphics,
inancials, and bo owing his o y a e p esen ed in AppendixF.
Fig. 6 SHAP alues o he ea u es Coun y_Lang (le ) and Educa ion ( igh ). The blue do s ep esen
he p edic ions o he boos ed model, while he lines a e he coe icien s o he linea model, wi h hei
s a is ical signi icance indica ed by he colo ba on he igh (colou igu e online)
Fig. 7 SHAP alues o he ea u e Age. The blue do s ep esen he p edic ions o he boos ed model,
while he slope o he line is de e mined by he coe icien o he linea model. I s s a is ical signi icance
is indica ed by he colo ba on he igh (colou igu e online)

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Coun y. The mos impac ul demog aphic ea u e is he coun y and language
o he bo owe . Fo his ea u e, he Shapley alues o he linea and boos ed Cox
model appea o be qui e simila in magni ude and di ec ion, excep o he cen-
e ing di e ence. While he boos ed model is cen e ed on he a e age con ibu ion
o all ea u e alues, he linea model is cen e ed on he i s ea u e alue d opped
in one ho encoding (i.e., EE). This esul s in sligh ly highe alues o he linea
model. The linea model’s SHAP alues a e equal o he coe icien s o he linea
Cox eg ession (see AppendixE).
Bo h models show ha Es onian-speaking Es onians ha e he lowes isk, ol-
lowed by Russian-speaking Es onians and Finnish bo owe s. Spanish bo owe s
exhibi he highes de aul isk
(HR ∗e1.2 ≈3.22).
Educa ion. One o he mo e in ui i e ea u es in he demog aphics ca ego y is
he educa ional le el o he bo owe . While he boos ed model inds a mono oni-
cally dec easing isk wi h highe educa ion, he linea model only inds a signi ican
impac on isk o he highes educa ional le el
(HR ∗e−0.2 ≈0.82).
Age. The linea model iden i ied age as a signi ican isk ac o o he
p=10−2
le el (blue line), and ound ha he isk dec eased mono onically wi h age. Fo
example, a bo owe aged 60
(𝜙age ≈−0.04)
would ha e a ound 92% he isk o a
bo owe aged 20
(𝜙age ≈0.04)
wi h
HR =e−0.04∕e0.04 ≈0.92.
By de ini ion, he
slope o he line co esponds o he coe icien o he linea Cox eg ession (−0.002)
and has i s x-in e cep a app oxima ely 40yea s, which is he a e age age o bo -
owe s. In he boos ed model he isk o de aul also gene ally dec eases wi h age.
Howe e , young bo owe s be ween 20 and 25 and bo owe s olde han 60 ha e a
highe isk han he linea model would p edic .
While hese SHAP dependence plo s isualize he indi idual ea u e’s con ibu-
ions, some ea u es may in e ac wi h o he ea u es in he model, leading o e ical
dispe sion in he plo s (e.g., o Coun y_Lang and Educa ion). These can be in es i-
ga ed u he using SHAP in e ac ion alues, as shown in he ollowing sec ion.
4.3 Model explana ions: SHAP ea u e in e ac ions
The SHAP in e ac ion e ec s es ima e how much he SHAP alue o a ea u e
changes when combined wi h ano he ea u e. Sub ac ing all in e ac ion e ec s
om he o al e ec s esul s in he mo e ocused main e ec o a ea u e. This main
e ec is o en mo e in e p e able han he o al e ec , as i is no in luenced by
in e ac ion e ec s and hus shows less e ical dispe sion.
In he plo s below, we p esen he main e ec and he wo mos impo an in e ac-
ion e ec s (which a e ou wo examples om he las sec ion, Coun y_Lang and
Age) o he ca ego ical ea u e wi h he mos e ical dispe sion, HomeOwne ship-
Type. Fo he in e ac ion e ec s, he do s in he sca e plo s a e colo ed by he alue
o he in e ac ing a iable. He e, ed indica es a highe and blue indica es a lowe
alue. The colo ing is illus a ed wi h he colo ba s on he igh .
Compa ed o he o al SHAP alue (see Appendix F), he main e ec o he
homeowne ship ype in Fig.8 shows less e ical dispe sion.
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Looking a he in e ac ion wi h he coun y (and language o Es onians), as seen
in Fig.9, bo owe s li ing wi h hei pa en s o in u nished apa men s a e deemed
Fig. 8 SHAP alues o he main e ec o HomeOwne shipType. The main e ec is calcula ed by sub-
ac ing all in e ac ion e ec s om he o al e ec ( o HomeOwne shipType, see AppendixF)
Fig. 9 SHAP alues o he in e ac ion e ec o HomeOwne shipType and Coun y_Lang. The do s a e
colo ed by he alue o Coun y_Lang (colo ba on he igh ) (colou igu e online)
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Digi al Finance (2024) 6:501–542
1 3
less isky in Finland and Spain, while he opposi e is ue o Es onians. The in e se
ela ionship is ound o he o he ca ego ies, excep o owne s. He e, Spanish bo -
owe s a e deemed mo e isky, ollowed by Es onians and Finns.
Figu e10 shows he in e ac ion wi h age. The isk dec eases o olde bo owe s
mos no ably in he ca ego iesMo gage and Owne , while inc easing o Li ing-
Wi hPa en s and Tenan Fu nished.
In summa y, hese in e ac ion e ec s e eal mo e in e p e able ea u e con ibu-
ions on c edi isk o less clea e ec s such as HomeOwne shipType. These in e -
ac ion e ec s a e de i ed om he boos ed model wi hou any manual modeling.
5 Discussion
The p incipal goal o his s udy was o e alua e he u ili y and pe o mance o
explainable ML su i al analysis wi hin he P2P lending sec o , wi h a pa icula
ocus on i s po en ial o imp o e isk assessmen and isk indica o analysis
compa ed o linea models.
5.1 Model pe o mance
Ou esul s show ha he ML model ou pe o med he linea model. This applies
o bo h Ha ell’s c-index and he mo e conse a i e IPCW c-index. While he
di e ences appea sligh o he c-indices, he ollowing esul s on p ac ical a ing
pe o mance demons a e ha he boos ed model pe o med signi ican ly be e
Fig. 10 SHAP alues o he in e ac ion e ec o HomeOwne shipType and Age. The do s a e colo ed by
he alue o Age (colo ba on he igh ) (colou igu e online)
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a isk assessmen . Fo an in-dep h analysis o he c-index esul s, including hei
limi ed signi icance in p ac ice and u he obus ness checks, see AppendixC.
The boos ed model achie ed he bes isk di e en ia ion ac oss he a ing g oups
and as ly ou pe o med Bondo a’s a ing. The Kaplan–Meie su i al es ima es
e ealed ha he boos ed model was he only model wi h non-c ossing su i al
cu es o de ed co ec ly by isk anking (Fig.5). He e, i had he la ges ma gins
be ween g oups, he smalles con idence bands and also he la ges span be ween
he highes and lowes isk g oups, indica ing a supe io abili y o disc imina e loans
by isk. When looking a he abula esul s including de aul - and IRR a e, com-
pa ed o Bondo a, he boos ed model showed a mo e o dinal, e en dis ibu ion and
wide sp ead o he IRR be ween he a ing g oups om 15.63 o −40.69% o he
boos ed-, and 3.91 o −36.26% o Bondo a’s a ings.
In es ing an equal amoun in boos ed “AA” a ed loans would ha e ou pe -
o med he Bondo a- a ed “AA” loans by almos 19% p.a. (IRR o 15.63% compa ed
o −3.20%). Mo eo e , he boos ed “AA” a ed loans we e less isky, a a de aul
a e o 14.45%, in con as o 17.26% o he Bondo a “AA” g oup. These esul s
we e especially s iking when conside ing he isk-g oup sizes. The boos ed model
assigned mo e han ou imes as many loans as Bondo a o he “AA” a ing (713 s
168). This a o able isk- e u n p o ile could be u he enhanced by a ge ing mis-
p iced loans (p edic ed low isk and high in e es a es). Fu u e esea ch could in es-
iga e he model’s po en ial o iden i ying misp iced loans on he seconda y ma ke .
On he opposi e spec um, ML su i al analysis a ings could aid in he sc eening
o high- isk bo owe s, add essing a majo challenge o P2P pla o ms. The
boos ed model a ed almos wice as many bo owe s as F, e u ning − 40.69%
annually compa ed o Bondo a’s F g oup a −36.26%. Sc eening ou hese high-
isk bo owe s would bene i in es o s, pla o ms and lowe - isk bo owe s alike, as
a gued in he heo y sec ion.
In addi ion, boos ed su i al analysis can enable ai e in e es a es on P2P pla -
o ms. Mul iple c ossing su i al cu es and poo p edic i eness o ime- o-de aul
indica ed ha he Bondo a a ings may no be well-calib a ed. This could cause
un ai in e es a es, as de ailed in Sec .2. I he in e es a es on loans we e ai ly
p icing isk, hey should compensa e o i . Howe e , we ound a di e en pic u e,
e.g., he a e age in e es a e o he boos ed “AA” g oup (27.77%) was almos h ee
imes ha o Bondo a’s “AA”-g oup (9.52%), despi e he boos ed-“AA” g oup’s
lowe de aul a e. Mo eo e , we obse ed a low co ela ion be ween de aul isk
and in e es a es. The a ing-pe o mance di e ences may be a ibu ed o he ac
ha Bondo a’s a ings encode expec ed loss a he han expec ed ime- o-de aul .
Howe e , expec ed loss is linked o expec ed ime- o-de aul , as a gued in he heo y
sec ion (Sec .2). Fu he mo e, he boos ed a ings ou pe o med Bondo a’s a ings
ega dless o he used pe o mance measu es (i.e., c-index, di e en ia ion based on
Kaplan–Meie cu es, mean IRR and mean de aul a e). Hence, he in e es a es
may be se inaccu a ely and bo owe s should ge quo es om mul iple pla o ms o
p omo e ai e p icing.
While he boos ed model ou pe o med he linea model, he linea model exhib-
i ed decen isk- a ing pe o mance, excep o “C” ha ing a signi ican ly highe
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Digi al Finance (2024) 6:501–542
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de aul a e (49.17%) han D (39.58%, AppendixD). We will add ess he model di -
e ences in he nex sec ion.
In summa y, he applica ion o boos ed su i al analysis o a e loans o igina ed
in 2020, u ilizing his o ical pe o mance da a a ailable o an in es o by he end
o 2019, demons a ed e ec i e esul s. Ou indings sugges ha , wi hin ou da a-
se , boos ed ML su i al analysis models eme ged as a p omising ool o imp o -
ing c edi isk assessmen , suppo ing in es o s’ decision-making, ad ancing isk
sc eening and p omo ing ai e in e es a es.
5.2 Model explana ions
Ano he objec i e o his s udy was o in es iga e whe he explainable ML su i al
analysis can be bene icial o isk indica o analysis in P2P lending. Wi h SHAP
explana ion alues, we explained and compa ed bo h linea and boos ed Cox models
using ea u e dependence plo s (Sec .4.2).
O e all, he boos ed model ex ac ed a leas as much in o ma ion om he
da a as he linea model. In ou da a, whe e he linea model iden i ied signi ican
e ec s, he boos ed model consis en ly ound simila e ec s (see AppendixF o
a ull display o all ea u e con ibu ions). Unsu p isingly, hese simila indings
a e mos ly in line wi h p io esea ch. To name a ew: Bo owing isk educed wi h
age (e.g., Albe & Du y, 2012; Ku nianingsih e al., 2015), male gende indica ed
highe isk (e.g., Lin e  al., 2017), while ha ing a mo gage educed isk (e.g.,
Se ano-Cinca e al., 2015).
Fu he mo e, he boos ed model unco e ed mo e de ailed and new ela ionships
be ween bo owe in o ma ion and de aul isk. Fo example, all g ades o educa-
ion we e well di e en ia ed by he boos ed model, wi h highe educa ion dec eas-
ing isk. This is in line wi h p io esea ch (e.g., Chen e al., 2018; Lin e al., 2017).
In con as , he linea model only ound a signi ican impac on isk o he highes
educa ional le el, and no signi icance o he in e media e le els. The same applied
o homeowne ship ype (Fig.12b), whe e he boos ed model clea ly dis inguished
Li ingWi hPa en s (highe isk), and Owne (lowe isk) in addi ion o he ca ego-
ies iden i ied signi ican by he linea model (Mo gage, lowe isk and Tenan Fu -
nished, highe isk). While he highe isk o bo owe s li ing wi h hei pa en s
makes in ui i e sense (indica es lowe asse s), he lowe isk o homeowne s is sup-
po ed by p io esea ch (e.g., Se ano-Cinca e al., 2015). Fu he mo e, some a i-
ables impac ed he boos ed model whe e he linea model did no ind signi icance
a all. The ela ionship wi h DTI (Fig.13b) ound by he boos ed model is a known
ac o in isk p edic ion (Emek e e al., 2015; Se ano-Cinca e al., 2015) and was
no iden i ied by he linea model.
In addi ion o he mo e de ailed linea e ec s, he boos ed model ound bo h
known and no el non-linea and in e ac ion e ec s explo a i ely. Fo example,
c edi isk dec eased sha ply o younge bo owe s wi h age, la ening ou un il he
age o 55 yea s and hen inc easing sligh ly again. As men ioned, esea ch con i ms
his gene al end o he models, as isk a e sion inc eases wi h highe age (e.g.,

521
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Digi al Finance (2024) 6:501–542
Albe & Du y, 2012; Ku nianingsih e al., 2015). Addi ionally, e idence poin s
owa ds a nonlinea and domain-speci ic ela ionship be ween isk- aking and age,
wi h inc eased isk- aking in ea ly adul hood (e.g., Rolison e al., 2014; Willoughby
e al., 2021), which was also picked up by he boos ed model. On op, he newly
quan i ied isk inc ease o bo owe s a 55yea s may be explained by lowe income
due o e i emen , inc eased medical cos s and educed li e expec ancy. Analyzing
in e ac ion e ec s also un eiled no el isk indica o s and helped us dissec he
e ical dispe sion o p ima y e ec s. Fo HomeOwne shipType, we ound ha
enan s li ing wi h hei pa en s o in a u nished apa men we e deemed less isky
when younge (Fig.10), which in ui i ely makes sense. The in e ac ion wi h he
coun y (Fig.9) indica es ha he model may be able o accoun o sys emic and
cul u al di e ences. To he bes o ou knowledge, hese pa icula in e ac ion e ec s
ha e no been iden i ied explo a i ely in p io esea ch. Especially in he Eu opean
ma ke , analyzing cul u al and sys emic di e ences (e.g., due o di e en e i emen
sys ems) migh be aluable o c edi isk assessmen .
Finally, one ad an age o he classical model is ha i can es o s a is ical sig-
ni icance. Howe e , in he cases whe e he ML-SHAP alues we e less dense, he
linea models o en ound he ea u e alue o be less o e en insigni ican (whi e
colo ing). This indica es ha SHAP ea u e impo ances (a e age absolu e SHAP
alues) may be consis en wi h s a is ical signi icance, which was also ound by
Bussmann e al. (2021).
O e all, he boos ed model no only ound he same signi ican isk ac o s as he
linea model bu also ound mo e de ailed and e en new ela ionships be ween isk
ac o s and de aul isk. This included nonlinea and in e ac ion e ec s ha a e no
quan i iable in linea models in he same explo a i e way.16 This is in line wi h p io
esea ch on his me hodology in oncology (Moncada-To es e al., 2021), suppo ing
he a gumen ha explainable machine lea ning su i al analysis can e eal known
and po en ially no el isk ac o s in isk esea ch.
5.3 Limi a ions andimplica ions
Fu he esea ch is equi ed o es hese me hods mo e widely. While we we e able
o achie e excep ional esul s on he Bondo a da ase , u u e s udies should es he
eliabili y o he models by applying hem o di e en da ase s and spli da es. Fo
he la e , we sugges a olling window app oach, as his would allow he adap abil-
i y and alidi y o he models o be es ed. He e, he US Lending Club da ase could
be sui able. The lending club da ase is widely used in p io esea ch and has a much
la ge numbe o comple ed loans anging o e a longe pe iod. The Bondo a da ase
did no allow o his a he ime o w i ing due o he limi ed a ailable obse a ion
pe iod combined wi h he need o comple ed loans o calcula e he IRR. Howe e ,
i can be e isi ed in he u u e, as he da ase g ows and mo e loans a e comple ed.
Fo ou pu poses, o assess isk a ing abili y and isk- ac o analysis he da ase we
16 While in e ac ion e ec s can be quan i ied in linea Cox eg ession, hey need o be ca e ully modeled
by hand based on domain knowledge and p io esea ch. This can be e y esou ce-consuming, espe-
cially wi h many ea u es.
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1 3
used is well-sui ed. Especially o he la e , as seen in he explana ions, he da ase
p o ided aluable hypo heses in o cul u al di e ences impo an o isk assessmen
in he Eu opean P2P ma ke ( his insigh would no be possible on he US Lending
Club da ase ). Fu he mo e, he good pe o mance o he ML models on he es
se despi e he changed isk p o ile (changes in a ing dis ibu ion in Fig.2) indi-
ca ed ha he models a e likely obus and can be used o u u e loans. As discussed
in mo e de ail in Appendix C, we also applied andom sampling and a ed 5-yea
loans, which esul ed in e en highe pe o mance o he ML models and quali a-
i ely simila esul s o he SHAP alues. Addi ionally, simply emo ing bo owe s
wi h missing and spa se alues om he da ase can in oduce bias o he model.
This is especially p oblema ic i he missingness is sys ema ic and should be in es-
iga ed o a oid bias agains demog aphics (e.g., in ou case, he excluded homeless
and Slo akian bo owe ). While ou decision o compa e he models lead o ollow-
ing he mo e es ic ed p ep ocessing s eps o he linea model, he boos ed model
can be ained (and p edic ) on incomple e and spa se da ase s in u u e use.
Fu he mo e, no all o he explained ela ionships, as shown in AppendixF, we e
s aigh o wa d. Some equi ed u he in es iga ion (e.g., using in e ac ion e ec s),
and some con adic ed in ui ion. Fo example, we ound a isk dec ease wi h la ge
liabili ies and an inc ease wi h la ge income. We suspec ha his is caused by
collinea i ies, e.g., wi h DTI.17 This indica es ha explainable ML indings need o
be alida ed, as Shapley alues explain he model, and no he da a di ec ly. I he
model inds complex ma hema ical ela ionships ha obscu e he ue unde lying
isk ac o s, explana ions may be incapable o iden i ying meaning ul isk indica o s
ha a e in ui i e, s aigh o wa d, and suppo ed by heo y. De eloping a model
wi h use ul explana ions may equi e some ial and e o —especially h ough
egula iza ion and adequa e da a p epossessing, including ea u e selec ion and
modeling o a iables likely ele an in eali y. Ne e heless, spu ious ela ions a e
no only ound in ML models bu also in linea models. To o e come his issue, a
hypo hesis-based app oach is commonly used wi h linea models. Fo explainable
ML me hods ma ching quan i a i e wi h quali a i e heo y is equally impo an ,
al hough i s explo a i e app oach allows de i ing hypo heses di ec ly, which should
be e i ied wi h exis ing heo y.
6 Conclusion
In his s udy, we used classical and ML su i al analysis o p edic de aul  iskin
P2P lending using a Eu opean da ase wi h o e 350,000 loans. We compa ed he
pe o mance o he models in ank co ela ion, classi ica ion, and c edi isk a ing.
We hen opened he ML models’ black box using SHAP o explain he pe o mance
di e ences and iden i y c edi isk indica o s.
17 While liabili ies do no con ain he applied amoun , he DTI a io does. A a ixed DTI a io, la ge
liabili ies may indica e a lowe ela i e loan amoun o a bo owe ’s inancial si ua ion. Addi ionally, DTI
may ypically dec ease wi h highe incomes, and hus, high DTI a la ge incomes may indica e highe
isk.
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Ou esul s demons a ed ha ML su i al analysis pe o ms excep ionally well
in c edi sco ing, signi ican ly ou pe o ming he pla o m’s isk a ings. Fo in es-
o s, ou a ings e ealed a p o i oppo uni y h ough a ge ing high-in e es loans
wi h low es ima ed isk. On he pla o m side, mo e accu a e isk assessmen s could
p omo e ai e p icing and imp o e he sc eening p ocess, ul ima ely educing o e -
all isk and inc easing po olio pe o mance.
Using SHAP, we we e able o explain he models decision making and disco e
bo h no el and known c edi isk ac o s. This yielded compelling and in ui i e
hypo heses, es ablishing p omising a enues o u u e esea ch.
Al oge he , he me hodology’s excep ional pe o mance esul s, combined wi h
i s meaning ul explana ions, con i med i s abili y o imp o e c edi - isk a ings
h ough mo e accu a e while anspa en c edi isk assessmen s. Wi h analogous
indings in oncology ha alida e explainable ML su i al analysis’ abili y o gen-
e a e knowledge, we a e con iden ha his app oach can u he he unde s anding
o ime- o-e en da a ac oss a ious domains. This me hodology could spa k a new
wa e o su i al analysis esea ch, including he eexamina ion o s udies p e iously
conduc ed wi h linea su i al analysis me hods.
Appendices
A Bondo a da ase ea u e desc ip ions
The ollowing able shows an exce p o he ea u es p esen ed in he loan da ase ,
g ouped by ca ego ies. The ea u es we e selec ed based on public a ailabili y and
ele ance o he analysis. Bondo a excluded 16 ea u es due o da a p o ec ion
egula ions s a ing on June 1, 2017. The excluded ea u es include in o ma ion
abou amily s a us, employmen , loan usage, and inancial de ails like sou ces o
income, ee cash, and deb - o-income (DTI) a io (Table2).
B De ailed explana ion o  heme hodology
This appendix explains he su i al analysis models used in his s udy in mo e de ail
and demons a es how classical models can be gene alized o allow o mo e complex
models using Machine Lea ning (ML). Finally, we in oduce he me hods used o
e alua e and explain he models.
B.1 Su i al analysis
S a is ical su i al analysis in es iga es he iming o an e en o in e es . This e en
can be any hing ha occu s o e ime, like dea h, ailu e o a machine, o c edi de aul .
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Table 2 Da a ea u es o he Bondo a loan da ase
G oup Name Desc ip ion
Applica ion and con ac de ails AppliedAmoun The amoun bo owe applied o o iginally
Con ac EndDa e The da e when he loan con ac ended
Fi s Paymen Da e Fi s paymen da e acco ding o ini ial loan schedule
LoanDa e Da e when he loan was issued
Bondo a a ing de ails Expec edLoss Expec ed Loss calcula ed by he cu en Ra ing model
Expec edRe u n Expec ed Re u n calcula ed by he cu en Ra ing model
HomeOwne shipType 0 Homeless 1 Owne 2 Li ing wi h pa en s 3 Tenan , p e- u nished p ope y 4 Tenan ,
un u nished p ope y 5 Council house 6 Join enan 7 Join owne ship 8 Mo gage 9 Owne
wi h encumb ance 10 O he
LossGi enDe aul Gi es he pe cen age o ou s anding exposu e a he ime o de aul ha an in es o is likely o
lose i a loan ac ually de aul s. This means he p opo ion o unds los o he in es o a e all
expec ed eco e y and accoun ing o he ime alue ...
P obabili yO De aul P obabili y o De aul e e s o a loan’s p obabili y o de aul wi hin a one-yea ho izon.
Ra ing Bondo a Ra ing issued by he Ra ing model
Bo owe demog aphics Age The age o he bo owe when signing he loan applica ion
Coun y Residency o he bo owe
Educa ion 1 P ima y educa ion 2 Basic educa ion 3 Voca ional educa ion 4 Seconda y educa ion 5 Highe
educa ion
Employmen S a us 1 Unemployed 2 Pa ially employed 3 Fully employed 4 Sel -employed 5 En ep eneu 6 Re i ee
Gende 0 Male 1 Woman 2 Unde ined
LanguageCode 1 Es onian 2 English 3 Russian 4 Finnish 5 Ge man 6 Spanish 9 Slo akian
NewBondo aCus ome ( enamed om
NewC edi Cus ome )
Did he cus ome ha e a p io c edi his o y in Bondo a 0 Cus ome had a leas 3 mon hs o
c edi his o y in Bondo a 1 No p io c edi his o y in Bondo a
Ve i ica ionType Me hod used o loan applica ion da a e i ica ion 0 No se 1 Income un e i ied 2 Income
un e i ied, c oss- e e enced by phone 3 Income e i ied 4 Income and expenses e i ied
C edi and bo owing his o y Amoun O P e iousLoansBe o eLoan Value o p e ious loans
NoO P e iousLoansBe o eLoan Numbe o p e ious loans
531
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Digi al Finance (2024) 6:501–542
be ween he p edic ed and he ac ual alue. This way, each ee ies o co ec he
e o o he p e ious ees. The ees can hen be combined using simple (weigh ed)
addi ion.
The XGBoos package used in his s udy is an implemen a ion o a boos ed
eg ession ee. XGBoos uses ML p inciples like egula iza ion o p e en o e -
i ing, and achie es b eak h ough pe o mance in speed and memo y usage using
(“ex eme”) op imiza ion me hods (Chen & Gues in, 2016).
B.5 Model explana ion using SHAP
E en hough ML me hods a e powe ul ools o p edic ion, hey a e o en consid-
e ed black boxes (Van Liebe gen, 2017). Fo example, he esul ing XGBoos mod-
els used in his analysis consis o up o 2594 ees wi h a maximum dep h o up o
10 node laye s. Wi h o e a million nodes
(2594 ∗29),
i is di icul o gauge how he
model makes i s p edic ions om he model pa ame e s. Ins ead, we can explain he
model by looking a he ea u e con ibu ions o he model ou pu . Tha is he di e -
ence in he p edic ion o he model wi h and wi hou ha ea u e.
This is qui e simple in he linea case. Fo example, he ea u e con ibu ions o a
ea u e
xj
in he model
(x)=𝛽0+𝛽1x1+
⋯
+𝛽pxp
is simply he p oduc o i s coe -
icien
𝛽j
and i s alue
xj,
minus he expec ed alue o his p oduc :
Fo mo e complex ML models like g adien boos ing, his is no as s aigh o wa d.
In ou example, he e ec o income on he ime o de aul could be dependen on
o he a iables, like he coun y o he bo owe . These in e ac ion e ec s a e o en
p esen in ML models, whe e he impac o a ea u e on model ou pu may depend
on he alues o o he ea u es. So how can we conside hese in e ac ion e ec s
when es ima ing he con ibu ion o each ea u e o he model ou pu ?
One solu ion o his p oblem s ems om coope a i e game heo y. Shapley alues
(Shapley, 1952) a e a unique solu ion o he p oblem o ai ly dis ibu ing he gain
(e.g., pay-o ) o a coope a i e game among i s playe s. In a coope a i e game, he
in e ac ions be ween he playe s a e impo an . One playe who wo ks well in a eam
may imp o e he p oduc i i y o he whole eam mo e han a playe who s uggles
wo king in a eam. Shapley’s alues ake hese e ec s in o accoun by compa ing he
achie emen s o he whole eam wi h and wi hou each playe . E e y playe is hen
assigned a Shapley alue ha ep esen s hei ma ginal con ibu ion o he ou come
(e.g., he es ima ed addi ional pay-o ha he eam achie ed wi h, compa ed o
wi hou he playe ). Thus, adding up all Shapley alues yields he o al gain o he
game. We can use his solu ion o ou p oblem o explaining ML p edic ions by
dis ibu ing he p edic ion con ibu ions (pay-o ) op imally among he ea u es
(playe s). See (Lundbe g e al., 2019) o de ails on his es ima ion in he XGBoos
case.
Shapley Addi i e Explana ions (SHAP) can es ima e pai -wise ea u e
con ibu ions as well, yielding he in e ac ion e ec s o any ea u e pai . By
emo ing hese in e ac ion alues om he SHAP alue o a ea u e, we can isola e
(7)
𝜙j(x)=𝛽jxj−E(𝛽jxj).

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Digi al Finance (2024) 6:501–542
1 3
he main e ec . The main e ec is o en easie o in e p e , while he in e ac ion
e ec s can help unde s and how a ea u e in e ac s wi h o he ea u es in a model.
We will use his app oach o wo ea u es in he esul s sec ion.
To explain he o e all decision-making o a model and no jus single p edic ions,
we can calcula e he SHAP alues o a la ge sample and analyze he global
ela ionship o ea u e alues and model ou pu (Lundbe g e al., 2020). In ou s udy,
we use SHAP dependence plo s o isualize ou models.
While o he me hods (e.g., LIME, Ribei o e al., 2016) can also be used o explain
ML models, SHAP has se e al p ope ies desi able o his analysis: Mos impo -
an ly, he SHAP amewo k is model agnos ic. This means ha i can be applied o
explain and compa e he p edic ions o any model, independen o he model’s inne
wo kings. Addi ionally, i is he only me hod ha can sa is y h ee desi able expla-
na ion a ibu es: local accu acy (single explana ions cap u e he di e ence be ween
expec ed model ou pu and he p edic ion), missingness (missing ea u es ge an
a ibu ion o ze o), and consis ency (i a changed model inc eases he impac o a
ea u e, i s SHAP alue will no dec ease). P o iding his unique solu ion o hese
c i e ia, Lundbe g and Lee’s SHAP amewo k uni ied six popula addi i e model
explana ion me hods, including LIME, a he ime o i s publica ion. Fu he mo e,
SHAP is well-op imized o some ML models. The XGBoos implemen a ion uses
g aphical p ocessing uni s o es ima e SHAP alues (Lundbe g e al., 2019). This
p o ides a signi ican speedup compa ed o o he me hods and makes i easible o
calcula e SHAP alues o la ge da ase s (Lundbe g e al., 2020) like he Bondo a
da ase used in his s udy.
C Model pe o mance: c‑index
This appendix akes a close look a he pe o mance o he models using he
conco dance index (c-index). We begin by discussing i s calcula ion and meaning.
Ha ell’s c-index (Ha ell e  al., 1982) measu es he ank co ela ion be ween
p edic ed isk sco es and he ac ual su i al imes. I is de ined as he a io o
conco dan pai s o compa able pai s. Two obse a ions a e compa able when we
can de e mine whe he one o he obse a ions has a sho e su i al ime han he
o he . A pai o compa able obse a ions is conco dan when he obse a ion wi h
he sho e su i al ime also has a highe p edic ed isk sco e. In o he wo ds, he
c-index is he p obabili y ha he model co ec ly p edic s he su i al o de o wo
andomly chosen loans. A c-index o 0.5 would indica e model andomness, while
a c-index o 1.0 would indica e pe ec ly igh and a c-index o 0.0 pe ec ly w ong
p edic ions.
While he c-index is a popula me ic o e alua ing su i al models, i has some
limi a ions. Wi h la ge numbe s o censo ed obse a ions, he c-index becomes oo
op imis ic (Uno e al., 2011). To accoun o his issue, Uno e al. (2011) p opose he
In e se P obabili y o Censo ing Weigh ing (IPCW) c-index ha akes he censo ing
dis ibu ion o he da a in o accoun . As we ha e ac i e, censo ed loans in ou da a-
se , we addi ionally use his es ima o o e alua e he models.
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Figu e11 p esen s Ha ell’s c-index and he mo e conse a i e censo ing inde-
penden IPCW c-index o all models. The esul s indica e ha he boos ed models
pe o m be e han he linea models. In addi ion, he inclusion o he Bondo a a -
ing only sligh ly imp o es pe o mance. This sugges s ha he a ings do no encode
much addi ional in o ma ion use ul o he models. Fu he mo e, he IPCW c-index
is sligh ly lowe han he egula c-index o all models. This is expec ed, as he
IPCW c-index is a mo e conse a i e measu e when a la ge numbe o subjec s is
censo ed.
In gene al, i is wo h no ing ha al hough he c-index o all models is
signi ican ly highe han 0.5 (i.e. no andom), i is s ill ela i ely low
(<0.7).
The
easons o his a e wo old. Fi s , while sampling he es a e he aining da a
p o ides a mo e ealis ic se ing, he po olios s ongly luc ua ing isk p o ile
and an o e all shi owa d less isky loans may be challenging o accoun o he
models. As a obus ness check, we e an he models wi h andom sampling, 5-yea
loans and mon hly ime pe iods, which esul ed in a c-index abo e 0.75. Second, by
de ini ion, he c-index is highly sensi i e o sligh di e ences in su i al ime. While
in p ac ice, a di e ence in loan su i al ime o one day likely does no ma e , i
can lowe he c-index i he loan isks a e no anked in he same o de . This again
illus a es ha he impo ance o hese indica o s should no be o e s a ed. In ou
case, he me ics in he main analysis (Sec .4.1) a e likely o be mo e ele an o
s akeholde s.
As a u he obus ness check, we es ed he pe o mance o ML AFT models
ins ead o Cox models. No ably, bo h pe o med e y simila ly. Howe e , we did
obse e ha he AFT model was mo e di icul o une as wo addi ional pa ame e s
ega ding he su i al dis ibu ion needed o be se . This slowed op imiza ion con-
e gence signi ican ly. The simila pe o mance suppo s he idea ha he models
Fig. 11 Ha ell’s c-index (le ) and he IPCW c-index ( igh ) o he models. “Lin_” p e ixes linea mod-
els, while “Bs _” p e ixes he boos ed models. Addi ionally, a “1” deno es models ha do no use he
Bondo a a ing a iables o hei p edic ion (which is ue o all models discussed in he main ex ).
A “2” deno es models ha also use he Bondo a a ing. We use he py hon package li elines (Da idson-
Pilon, 2023) o es ima e he c-indices
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Digi al Finance (2024) 6:501–542
1 3
a e simila ly es ic ed because hey canno model ime- a ying e ec s. As he p o-
po ional haza ds assump ion o he Cox model may be iola ed, u he esea ch
could in es iga e whe he less es ic i e models could pe o m be e in his con-
ex . Fo example, ins ead o se ing he su i al ime o ea ly epaymen o he loan
du a ion, epaymen s could be p edic ed and modeled as a compe ing isk. O he
classical models ha pe o med well on loan da a (Di ick e al., 2017) could be
implemen ed and es ed as ML models, and ad anced ML-models like boos ed su -
i al ees (Bai e al., 2022) may yield imp o ed esul s.
O e all, he pe o mance esul s suppo he indings o p io li e a u e ha ML
models can pe o m a leas as well as linea su i al analysis models (Moncada-
To es e al., 2021) while showing good esul s when used as classi ica ion models
(Bai e al., 2022).
D Model pe o mance: linea a ing model
See Table3.
E Coe icien s o  helinea Cox models
The ollowing able p esen s he esul s o he linea Cox model. S a s indica e he
s a is ical signi icance o he coe icien s. The able shows he coe icien s o he wo
linea models (wi h and wi hou Bondo a a ings) and he s anda d e o s in pa en-
heses (Table4).
Table 3 Mean alues g ouped by linea Cox a ings
The able includes he numbe o loans, he mean amoun , in e es a e, de aul a es and IRR o each
g oup. Loan s a us o he de aul a e and IRR is based on he app oach o Dömö ö e al. (2023). The
HR h esholds a e shown in pa en heses
Ra ing Coun
Amoun
In e es
(%)
De aul s
(%)
IRR
(%)
AA: (−in , 0.55] 858 2005.78 28.20 15.85 13.23
A: (0.55, 0.65] 906 2364.26 28.77 24.72 10.55
B: (0.65, 0.75] 1020 2589.93 28.90 34.51 6.45
C: (0.75, 0.97] 907 2518.62 30.73 49.17 −0.69
D: (0.97, 1.51] 768 2848.00 37.55 39.58 −3.25
E: (1.51, 2.1] 1412 2961.59 39.38 57.01 −18.95
F: (2.1, in ] 331 2791.44 50.01 77.64 −47.04
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Table 4 Cox p opo ional haza d model coe icien s
Pa ame e s Cox_1 Cox_2
IncomeTo al −0.0 (0.0) −0.0 (0.0)
Deb ToIncomeModeled 0.0 (0.0005) 0.0 (0.0)
Liabili iesTo al 0.0 (0.0) −0.0 (0.0)
Exis ingLiabili ies 0.0106* (0.0033) −0.0 (0.0)
AppliedAmoun 0.0*** (0.0) 0.0 (0.0)
Amoun O P e iousLoansBe o eLoan 0.0 (0.0) −0.0 (0.0)
P e iousRepaymen sBe o eLoan 0.0* (0.0) 0.0 (0.0)
Repaymen Ra io −0.7338*** (0.0533) −0.5419*** (0.0395)
P e iousEa lyRepaymen sBe oleLoan 0.0* (0.0) 0.0 (0.0)
NoO P e iousLoansBe o eLoan −0.0353*** (0.0075) −0.0285*** (0.0058)
P e iousEa lyRepaymen sCoun Be o eLoan −0.1977*** (0.0403) −0.06* (0.0262)
Coun y_Lang_EE_Ru 0.1866*** (0.0332) 0.0696* (0.0343)
Coun y_Lang_ES 0.9406*** (0.0416) 1.1699*** (0.0276)
Age −0.0007 (0.0009) −0.002* (0.0009)
Coun y_Lang_FI 0.7053*** (0.0331) 0.888*** (0.0269)
Gende _male 0.1497*** (0.0252) 0.0757* (0.0243)
Gende _unde ined 0.1895*** (0.0424) 0.0938* (0.0425)
Educa ion_Basic 0.0205 (0.0497) 0.0478 (0.0434)
Educa ion_Voca ional −0.1239** (0.0343) −0.0 (0.0)
Educa ion_Seconda y −0.0875* (0.0318) −0.0 (0.0)
Educa ion_Highe −0.3069*** (0.0328) −0.2082*** (0.0207)
Employmen Du a ionCu en Employe _Re i ee 0.1291* (0.0543) 0.0157 (0.0424)
Employmen Du a ionCu en Employe _T ialPe iod 0.0355 (0.1262) 0.0 (0.0003)
Employmen Du a ionCu en Employe _UpTo1Yea 0.0171 (0.0457) 0.0 (0.0001)
Employmen Du a ionCu en Employe _UpTo2Yea s 0.0161 (0.0586) −0.0 (0.0001)
Employmen Du a ionCu en Employe _UpTo3Yea s 0.0116 (0.062) −0.0 (0.0001)
Employmen Du a ionCu en Employe _UpTo4Yea s −0.0346 (0.0716) −0.0 (0.0002)
Employmen Du a ionCu en Employe _UpTo5Yea s 0.0293 (0.0447) 0.0 (0.0001)
Employmen Du a ionCu en Employe _
Mo eThan5Yea s
−0.0484 (0.0431) −0.0624* (0.0204)
HomeOwne shipType_Li ingWi hPa en s −0.014 (0.0409) 0.0 (0.0001)
HomeOwne shipType_Council house −0.1425 (0.1014) −0.0 (0.0003)
HomeOwne shipType_Tenan No Fu nished −0.0821 (0.0645) −0.0 (0.0002)
HomeOwne shipType_Tenan Fu nished 0.0868* (0.0384) 0.1076*** (0.026)
HomeOwne shipType_Join enan 0.0502 (0.0877) 0.0 (0.0003)
HomeOwne shipType_Join owne ship 0.0673 (0.0684) 0.0 (0.0002)
HomeOwne shipType_Mo gage −0.28*** (0.043) −0.1727*** (0.0319)
HomeOwne shipType_Owne , encumb ance −0.476** (0.135) −0.2549* (0.115)
HomeOwne shipType_Owne −0.1273** (0.0373) −0.0794* (0.0247)
Ve i ica ionType_income 0.0376 (0.0454) −0.0204 (0.0404)
Ve i ica ionType_income and expenses −0.0269 (0.0206) 0.0 (0.0)
NewBondo aCus ome _T ue −0.0246 (0.0279) 0.076* (0.0268)
NanRepaymen His o y_T ue −0.2317*** (0.0273) −0.1922*** (0.027)
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Table 4 (con inued)
Pa ame e s Cox_1 Cox_2
NanEa lyRepaymen _T ue −0.3377*** (0.028) −0.2455*** (0.0246)
In e es 0.0021* (0.0007)
Expec edLoss 0.0211 (0.2302)
Expec edRe u n −0.5082* (0.2032)
P obabili yO De aul 1.2587*** (0.115)
LossGi enDe aul −0.3897*** (0.0475)
Ra ing_A 0.0235 (0.0577)
Ra ing_B −0.0065 (0.0478)
Ra ing_C 0.0792 (0.0457)
Ra ing_D 0.276*** (0.046)
Ra ing_E 0.2142*** (0.0502)
Ra ing_F 0.2208*** (0.0567)
Ra ing_HR 0.0201 (0.0755)
Obse a ions 31517 31517
c_cph ain 0.711838 0.701238
c_cph es 0.665275 0.659625
LR 5973.63661 4449.765007
LR_p 0.0 0.0
*
p
<
0.01;
**
p
<
0.001;
***
p
<
0.0001
Fig. 12 SHAP alues—demog aphics

537
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F Dependence plo s o all ea u es
In his appendix, he dependence plo s o all ea u es o he ca ego ies demog aph-
ics, inancials, and bo owing his o y a e p esen ed. Wi hin ca ego ies, he plo s
a e o de ed by he magni ude o hei mean absolu e SHAP alue (i.e., ea u e
impo ance).
Demog aphics O e all he Shapley alues o he linea and boos ed Cox model
appea o be qui e simila in magni ude and di ec ion o he demog aphic ea u e
con ibu ions(Fig.12), excep o cen e ing di e ences (e.g., o coun y). Addi ion-
ally, he boos ed model shows e ical dispe sion, he la ges o e all o he home-
owne ship ype indica ing in e ac ion e ec s. The ain isibili y in some ca ego ies
o he boos ed model (e.g., T ailPe iod) is caused by he small coun p esen in he
aining se . In hese cases, he linea models ound he ea u e o be less o e en
insigni ican (blue colo ing). The boos ed model ound a nonlinea i y o he ea u e
in e ac ion wi h age.
Financials Fo he inancials, he di e ences be ween he linea and boos ed
models a e mo e appa en . The boos ed model ound nonlinea ela ionships whe e
he linea models ound no signi ican ela ionship a all (Fig. 13a–c). Exis ing
liabili ies we e ound o dec ease isk un il 3–5 liabili ies, and hen inc ease isk
sligh ly (Fig.13e). The e i ica ion ype (Fig.13 ) had a small impac on he isk,
wi h a sligh dec ease o e i ied bo owe s.
Bo owing his o y Rega ding he bo owing his o y, he models again ind simi-
la ela ionships (Fig.14a, d, , g). Howe e , again he e a e wo ea u es no ound
Fig. 13 SHAP alues— inancials
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1 3
e y signi ican in he s a is ical model bu qui e impo an in he boos ed model
(Fig.14b and c).
Au ho con ibu ions The ini ial idea and concep o he s udy was de eloped by GBW unde he guid-
ance o FR. GBW conduc ed he ini ial li e a u e esea ch, analyzed he da a, buil he p edic ion and
a ing models, calcula ed he Shapley alues, and p epa ed all igu es using Py hon and CUDA. GBW
w o e he i s d a o he pape as pa o a hesis, which FR supe ised. Subsequen ly, FR con ibu ed o
he u he de elopmen o he me hodology, in pa icula ega ding inancial aspec s, and he inal d a .
Bo h au ho s e iewed and app o ed he inal manusc ip .
Funding Open Access unding enabled and o ganized by P ojek DEAL.
Da a a ailabili y All da ase s used in his s udy we e ob ained om publicly a ailable da a sou ces (see
e e ences in Sec ion3).
Fig. 14 SHAP alues—bo owing his o y
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Digi al Finance (2024) 6:501–542
Decla a ions
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