An open innovation intraday implied volatility for pricing Australian dollar options

Le, Thi; Hoque, Ariful; Hassan, Kamrul Article An open innovation intraday implied volatility for pricing Australian dollar options Journal of Open Innovation: Technology, Market, and Complexity Provided in Cooperation with: Society of Open Innovation: Technology, Market, and Complexity (SOItmC) Suggested Citation: Le, Thi; Hoque, Ariful; Hassan, Kamrul (2021) : An open innovation intraday implied volatility for pricing Australian dollar options, Journal of Open Innovation: Technology, Market, and Complexity, ISSN 2199-8531, MDPI, Basel, Vol. 7, Iss. 1, pp. 1-14, https://doi.org/10.3390/joitmc7010023 This Version is available at: https://hdl.handle.net/10419/241608 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Open Innovation: Technology, Market, and Complexity Article An Open Innovation Intraday Implied Volatility for Pricing Australian Dollar Options Thi Le , Ariful Hoque * and Kamrul Hassan   Citation: Le, T.; Hoque, A.; Hassan, K. An Open Innovation Intraday Implied Volatility for Pricing Australian Dollar Options. J. Open Innov. Technol. Mark. Complex. 2021,7, 23. https://doi.org/10.3390/ joitmc7010023 Received: 10 December 2020 Accepted: 5 January 2021 Published: 9 January 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Murdoch Business School, Murdoch University, Perth 6150, Australia; [email protected] (T.L.); [email protected] (K.H.) *Correspondence: [email protected] Abstract: This study introduces the intraday implied volatility (IV) for pricing the Australian dollar (AUD) options. The IV is estimated using the at-the-money one-month, two-month, and threemonth maturity AUD options traded in the opening, midday, and closing period of a trading day. The Mincer-Zarnowitz regression test evaluates the predictive power of IV to forecast the foreign exchange volatility for the within-week, one-week, and one-month horizon. The mean absolute error, mean squared error, and root mean squared error measures are employed to assess the performance of IV in estimating the price of currency options for the within-week, one-week, and one-month horizon. This study reveals four critical findings. First, a three-month maturity IV does not contain vital information for pricing options. Second, IV incorporated information is not relevant to compute the value of options for a horizon of less than a week. Third, IV in the closing period of Monday or Tuesday subsumes most of the essential information to estimate options price. Fourth, the shorter (longer) maturity IV provides critical information to price options for the shorter (longer) horizon. The intraday IV is a new dimension of unobservable volatility in accurately pricing currency options for researchers and practitioners. Keywords: intraday implied volatility; realised volatility; Australian dollar options; Mincer–Zarnowitz regression 1. Introduction This study introduces intraday implied volatility (IV) which is an innovative approach to estimate the volatility of underlying currency for pricing currency options accurately. The intraday IV captures the market information at the opening, midday, and closing period of a trading day for pricing options with higher accuracy. If the options are mispriced, particularly overpriced options, it will increase the cost for hedging using currency options. The 2019 Bank for International Settlement (BIS) Triennial Survey results reveal that the turnover in Australian dollar (AUD) options increased by 58 percent between April 2016 and April 2019 [ 1 ], which is significant compared to other currency options. Therefore, Australian dollar options are considered to assess the capability of intraday IV to holding appropriate market information for pricing options precisely. Foreign exchange (FX) risks are reported as one of the major risks related to foreign investments and international assets pricing [ 2 ]. Most portfolio managers have been using FX options as their primary hedging tools to manage these risks [ 3 ]. The flexibility of currency options in creating a customised risk/return profile to achieve a specific investment objective has led to the significant growth of the FX options market. Holding currency options for various investment decisions such as hedging or speculation can be costly if the options are mispriced. Options mispricing affects the selection of hedge ratio, hedging efficiency, as well as expected hedging costs [ 4 ]. For this reason, the accuracy of currency options pricing has been attracting the attention of market participants [ 5 ]. Currently, the most commonly used model to calculate European options prices is known as the Black–Scholes [ 6 ] (BS) J. Open Innov. Technol. Mark. Complex. 2021,7, 23. https://doi.org/10.3390/joitmc7010023 https://www.mdpi.com/journal/joitmc J. Open Innov. Technol. Mark. Complex. 2021,7, 23 2 of 14 model [ 7 ]. The BS model assumes constant volatility. If true, this assumption would lead to a flat implied volatility curve. Observed implied volatility in practice differs across option contracts, depending on both moneyness and time to maturity. However, due to the theoretical approximation between the stochastic volatility and conditional volatility models to BS for at-the-money (ATM) options and nearest to expiration [ 8 , 9 ] and the rich informational content, implied volatility is still of interest [10–13] and the BS model is still widely applied [ 14 ]. Using the Merton [ 15 ] version of the BS model (BSM) to calculate prices of European currency options, all components are observable except the volatility of the underlying currency. Errors in the estimation of volatility result in the options mispricing [ 16 – 18 ]. The improvement of volatility estimation leads to lower errors of option prices [ 19 ]. Hence, forecasts of future volatility of underlying assets are vital for estimating and forecasting the currency options price accurately. The literature has explored the volatility intensively. As the options prices reflect the market’s expectation about the future movements of the prices of the underlying asset over the remaining life of the option contract, more research concentrates on volatility implied in options prices [ 20 ]. The implied volatility (IV) contains all available information, including historical data [ 10 , 20 – 25 ]. It is widely accepted that the IV from the market options price is a reasonable measure of the market’s opinion of the volatility of the underlying asset. The forward-looking IV subsumes relevant information in terms of future volatility, and it often outperforms historical volatility in predicting future realised volatility (RV). Such superior performance was recognised in different types of assets [ 26 ]. For currency options, the majority of both previous and more current research found that IV was a reliable predictor of future volatility. IV contained valuable information for volatility forecasting and captured approximately 50 per cent of actual currency volatility [27]. However, most of the previous research used the conventional approach that was based on daily IV obtained from daily closing options prices. As the operation of financial markets during their opening trading hour are based on a continuous, high-frequency basis, the conventional method using a discrete sample of datasets on markets at a significantly lower frequency with the majority of data being extracted per day, or per week to forecast volatility is no longer relevant [ 28 ]. New technologies have been creating opportunities to obtain better, faster, and more efficient datasets to explore financial market phenomena at the finest levels of data [ 29 ]. It provides reliable intraday data to supporting financial investment decisions across different assets classes and instruments consisting of commodities, derivatives, equities, fixed income, and foreign exchange [ 30 ]. The purpose of this paper is to investigate the performance of the intraday implied volatility (IV) for pricing the Australian dollar (AUD) options. This study has three major contributions. First, this study introduces an intraday IV approach based on the one-month, twomonth, and three-month maturity options traded in the opening, midday, and closing period of a trading day, which captures the most relevant information of the FX in estimating options prices. Second, the research findings indicate that the one-month and two-month maturity intraday IV holds vital information to predict the volatility of the underlying currency of options for the one-week and one-month forecast horizon, respectively. Third, this research confirms that the information content embedded in the IV based on the one-month and two-month maturity options is appropriate to estimate the value of currency options for the one-week and one-month horizon, respectively. The rest of the paper proceeds as follows. Section 2discusses the literature review. The next section describes the methodology and data used in this study. Section 4conducts the empirical analysis, followed by the discussion of the findings. The last section concludes the paper. 2. Literature Review Xu and Taylor [ 31 ] examined the informational efficiency of the four currency options (British pound (GBP), Deutsche mark (DEM), Japanese yen (JPY), and Swiss franc (CHF) against the US dollar (USD)) from January 1985 to January 1992 and concluded that J. Open Innov. Technol. Mark. Complex. 2021,7, 23 3 of 14 option prices subsumed useful information about future volatilities. Likewise, Jorion [ 32 ] tested the predictive power of DEM, JPY, and CHF against the USD and found that IV contained more information content compared to statistical time-series models. Kazantzis and Tessaromatis [33] analysed the information content and predictive power of IV using six currency options (JPY, DEM, GBP, CHF, Canadian dollar (CAD), and AUD against the USD) from December 1989 to April 1997. The findings indicated that IV was more informative than historical and GARCH-based volatilities for horizons ranging from one day to three months. Kim and Kim [ 34 ] showed that the IV of the CAD, CHF, DEM, GBP, and JPY options tended to be low in the early part of the week but remain high in the last part of the week beginning on Wednesdays. Chang and Tabak [ 35 ] produced evidence that the IV of Brazilian options contained vital information that was missing in the econometric models and it provided superior foreign exchange (FX) forecasts. Busch et al. [ 23 ] explored the role of IV in predicting future volatility and found that IV was an unbiased predictor and provided helpful information for volatility forecasting in the FX market. Pilbeam and Langeland [ 36 ] recognised that the IV of CHF, EUR, GBP, and JPY provided a superior performance compared to the GARCH model in both the low and high volatility periods of the FX market. Sahoo and Trivedi [ 37 ] showed that IV outperformed historical volatilities in forecasting future RV. Wong and Heaney [ 38 ] found the knowledge of the volatility smile, which were implied from the one-month maturity of GBP/USD, EUR/USD, AUD/USD, and USD/JPY options, improved FX volatility forecast accuracy. Covrig and Low [ 39 ] used over-the-counter (OTC) data for USD per GBP, JPY per USD, and USD per AUD to examine the information of IV for different forecast horizons. They suggested that quoted IV subsumed the information content of historically based forecasts at shorter horizons (one-month and two-month horizon). Pong et al. [ 40 ] found that the IV of the DEM, GBP, and JPY options incorporated most of the relevant information for the forecast horizon of either one-month or three-month. Christoffersen and Mazzotta [ 41 ] revealed that the IV of at-the-money (ATM) options for the EUR, GBP, and JPY mostly provided the unbiased and reasonably accurate forecasts of actual volatility one month and three months out. Until the late 1970s, using monthly data played an essential role in empirical research due to the unavailability of and access problems to higher frequency data, such as daily or intraday data. However, the development of information technology in the 1990s provided access to time-stamped observations on all quotes and transactions. These tick-by-tick data, termed as ultra-high-frequency data by Engle [ 42 ], are usually referred to as highfrequency data in current studies. High-frequency data indicated that many financial assets experienced the particular intraday patterns [ 20 ] and these patterns were significantly associated with intraday returns variations, volatility, volume, and bid-ask spreads [ 43 ]. A large number of studies suggested that intraday trading activities exhibited a U-shaped pattern with the trading volumes being extremely high at the market’s opening and closing periods, such as Wood et al. [ 44 ], Gerety and Mulherin [ 45 ], Brock and Kleidon [ 46 ] for the New York Stock Exchange (NYSE); Mclnish and Wood [ 47 ] for the Toronto Stock Exchange; and Hamao and Hasbrouck [ 48 ] for the Tokyo stock exchange. Several studies reported the M-shaped [ 29 , 49 ] or J-shaped patterns [ 50 ] for the UK stock exchange. Most of the research found the importance of intraday data in improving volatility predicting. There was a significant amount of information in the five-minute returns when estimating hourly variances [ 51 – 53 ]. Wang and Wang [ 20 ] explored the capability of intraday IV information content using the S&P500 Index as a sample from 2005 to 2010. Their study recognised that the IV around noon contains more useful information regarding future volatility than IV at the market’s closing period, which has been frequently used in the previous literature. Trading at a specific time of the trading day is motivated by specific information and risk factors, which do not remain during other times. Hence, our paper investigates the performance of IV in estimating and forecasting options prices at three different trading time periods of the trading day (opening, midday, and closing) using the AUD currency options datasets covering the period from 2010 to 2017. J. Open Innov. Technol. Mark. Complex. 2021,7, 23 4 of 14 Previous studies focused on the daily IV of currency options to forecast the volatility of FX. There are not many pieces of research utilising the high-frequency data and intraday IV in estimating and forecasting volatility. Furthermore, IV incorporated information has not been used for pricing options. Therefore, this paper will examine the capability of intraday IV with different time to maturity in forecasting future volatility and estimating currency options price. 3. Materials and Methods 3.1. Data Description This study used AUD currency options provided by the Options Price Reporting Authority (OPRA) as the last-sale options quotations. We obtained data from Thomson Reuters’ database through the Securities Industry Research Centre of Asia-Pacific (SIRCA). The sample period began on 01 January 2010 and ended on 31 December 2017. The options were traded on Monday to Friday, excluding public holidays from 9:30 to 16:00 (US Eastern standard time), and expired on the third Friday of each month. The options were European style, with the contract size of sample currency options being AUD 10,000 and settled in USD. The time to maturity of an option was assumed to be the number of calendar days remaining until the option matured. The sample options expired in one-month (2 to 30 days), two-month (31 to 60 days), and three-month (61 to 90 days) periods. The IV was calculated for the opening-period (9:30 to 10:00), midday-period (12:30 to 13:00), and closing-period (15:30 to 16:00) of a trading day. The time difference between “openingperiod” and “midday-period” and between “midday period” and “closing period” was equal (two and half hours) enough to position them evenly in a trading day. The BSM model assumed the volatility as constant, which introduced a bias into the IV estimation. Hull and White [ 54 ] stated that the magnitude of the bias in the BS model was the smallest for near-the-money options. Therefore, the IV was calculated based on the ATM one-month, two-month, and three-month maturity options traded during the opening, midday, and closing periods of a trading day. We followed the ATM criteria in Xing et al. [ 55 ]; the ratio of the strike price to the stock price was considered between 0.95 and 1.05. The average of the close bid/ask quote of each five-minute interval was computed for each options price to mitigate problems due to bid/ask bounce [ 56 ]. The one-month, two-month, and three-month AUD and USD deposit interest rate were used as the proxy of the risk-free interest rate. 3.2. Methodology The research methodology consists of five sub-sections, (i) calculating IV, (ii) computing realised volatility (RV), (iii) IV forecasting RV, (iv) IV estimating options model price, and (v) estimating the options pricing error. 3.2.1. Implied Volatility Calculation The BSM model replaces the stock price with foreign currency and considers the interest gained on holding foreign currency to be equivalent to a continuously paid stock dividend. The notation of the BSM model and its descriptions are as follows: Ct= price of call in domestic currency at time t Pt= price of put in domestic currency at time t St= spot price at time t Xt= exercise price in domestic currency at time t Rd t= interest rate of domestic currency at time t Rf t= foreign currency interest rate at time t T= options expiration time σt= volatility of underlying currency N= cumulative normal distribution function J. Open Innov. Technol. Mark. Complex. 2021,7, 23 5 of 14 In the BSM model, the European type call and put options are priced as: Ct=Ste−Rf tTN(d1,t)−Xte−Rd tN(d2,t)(1) Pt=Xte−Rd tTN(−d2,t)−Ste−Rf tN(−d1,t)(2) where, d1,t=lnSt Xt+Rd t−Rf t+σ2 t 2T σt√T, (3) And d2,t=lnSt Xt+Rd t−Rf t−σ2 t 2T σt√T=d1,t−σt√T(4) For notation convenience, let ξt=e−Rf tT and ηt=e−Rd tT so that Equations (1) and (2) can be written as follows: Cmkt,k,l t=StξtNhd1,tσk,l c,ti−XtηtNhd2,tσk,l c,ti (5) Pmkt,k,l t=XtηtNh−d2,tσk,l p,ti−StξtNh−d1,tσk,l p,ti (6) where ∀mkt = call and put market price; ∀k= one-month, two-month, three-month maturity options; ∀l= opening period, midday period, closing period. Now we calculate the implied volatility σk,l c,t for the ATM call options market price (Cmkt,k,l t) and implied volatility σk,l p,t for the ATM put options market price (Pmkt,k,l t) through the Newton–Raphson [ 57 ] iterative search procedure. Despite the numerous suggestions about weighted-average techniques for calculating IV, there is no theoretically appropriate weighting scheme in the literature to estimate IV. We used the method suggested by Jorion [ 32 ] that computes IV as the average of the call options price IV and the put options’ price IV. This study estimates IV as: ˆ σk,l t=ˆ σk,l c,t+ˆ σk,l p,t 2, (7) 3.2.2. Realised Volatility Calculation The actual market volatility is unobservable, so in evaluating volatility estimating and forecasting, the usual proxy for “true volatility” is the so-called realised volatility (RV). The RV sums the squared intraday returns sampled at a particular rate of recurrence [ 52 , 58 ]. The optimal interval to construct the RV is not known. Based on standard practice and previous literature, there is evidence that the five-minute RV as the benchmark outperformed other measures, and it is difficult to significantly surpass the five-minute (5 min) data frequency for RV [ 53 ]. Consequently, this study used daily RV series constructed from five-minute intraday spot prices as a proxy for the unobservable variance. If Si is the spot rate for a five-minute sampling frequency, the underlying exchange rate return in a five-minute interval was estimated as: ri,t=lnSi Si−1(8) where ri,t represents the return in interval ion day t. Equation (7) computed the realised variance of day t, vt= n ∑ i=1 r2 t,i, (9) J. Open Innov. Technol. Mark. Complex. 2021,7, 23 6 of 14 where n denotes the total number of data points from 9:30 to 16:00 for Monday to Friday. Further, the RV is the standard deviation of the realised variance. Therefore, the RV per trading day is calculated as: ˆ σRV t=√vt, (10) As intraday data of trading days estimate the RV, when the exchange is closed, days are ignored and the RV per annum is: ˆ σRV t=√Dvt, (11) where Dis considered 252 trading days per year consistent with the normal assumption of the options market. 3.2.3. Implied Volatility Forecasting Realised Volatility For IV from different maturities of options, the forecasting evaluation was implemented using the regression test introduced by Mincer and Zarnowitz [ 59 ], known as the Mincer–Zarnowitz (MZ) regression. In the MZ regression analysis, the RV is regressed on a constant and IV as in Equation (12): ˆ σRV t=β0+β1ˆ σk,l t−j+εt, (12) where ∀j= within-week, one-week, and one-month horizon. The within-week horizon indicates that the IV is calculated one to four days before the date of RV is computed. Similarly, the one-week and one-month horizon imply that the IV is estimated one week and one month before the date of RV is obtained. The MZ regression allowed the evaluation of two different aspects to predict the volatility. First, the unbiasedness and efficiency of the forecast were evaluated by testing the intercept and slope through the joint hypothesis (H 0 : β0 = 0 and β1 = 1) [ 60 ]. Second, the accuracy of the forecast was evaluated by the high goodness of fit value, R-squared (R 2 ). The R 2 is a statistical measure that represents the percentage of the variance for RV explained by IV. The value of R 2 compares the predictive power of IV to forecast RV for different horizons; such as, the R 2 of IV for the one-week horizon being higher than that of the one-month horizon implies that the RV can be explained well by the IV for the one-week horizon; that is, IV forecast of RV for oneweek horizon outperforms its performance for the one-month horizon. The MZ regression analysis uses the OLS (ordinary least squared) method with Newey–West corrected errors for heteroscedasticity and serial correlation. 3.2.4. Implied Volatility Estimating Options Model Price This study calculated the call options and put options model price using the estimated value of IV as the input for the BSM options pricing model. The Cmkt,k t and Pmkt,k t in Equations (5) and (6) were substituted with call options model price ˆ Πmod,k c,t and put options model price ˆ Πmod,k p,tas in Equations (13) and (14), respectively. ˆ Πmod,k c,t=StξtNhd1,tˆ σk,l t−ii−XtηtNhd2,tˆ σk,l t−ii (13) ˆ Πmod,k p,t=XtηtNh−d2,tˆ σk,l t−ii−StξtNh−d1,tˆ σk,l t−ii (14) 3.2.5. Options Pricing Error Estimation The options pricing error (OPE) is the difference between the ATM options market price and the estimated options model price. The OPE is measured using standard statistical J. Open Innov. Technol. Mark. Complex. 2021,7, 23 7 of 14 accuracy criteria, including mean absolute error (MAE), mean squared error (MSE), and the root mean squared error (RMSE), as in Equations (15)–(17), respectively. MAEm,k,l u=1 n n ∑ t=1ΠATM,k,l u,t−ˆ Πmod,k,l u,t(15) MSEm,k,l u=1 n n ∑ t=1ΠATM,k,l u,t−ˆ Πmod,k,l u,t2(16) RMSEm,k,l u=s1 n n ∑ t=1ΠATM,k,l u,t−ˆ Πmod,k,l u,t2(17) where ∀u=call price, put price. 4. Results Table 1describes the performance of IV to forecast RV for the within-week forecast horizon, one-week forecast horizon, and one-month forecast horizon. R 2 values from the forecasting regression in Equation (12) are reported. The IV with the highest R 2 is preferred. For the within-week forecast horizon, in the opening of Tuesday, three-month ( R2= 0.336 ) maturity IV outperformed in forecasting the RV. In the midday of Wednesday, two-month ( R2= 0.335 ) maturity IV outperformed in forecasting the RV. In the closing period of Monday, two-month (R 2 = 0.379) maturity IV performed better when predicting the RV. Overall findings for the within-week horizon indicated that the two-month maturity IV (R 2 = 0.379) in the closing period of Monday (begin-week day) were the most superior to the forecast of RV. For the one-week forecast horizon, in the opening period of Tuesday, one-month (R 2 = 0.465) maturity IV performed better in forecasting RV. Likewise, in the midday period of Tuesday, one-month (R 2 = 0.432) maturity IV showed better performance when predicting RV. Next, in the closing period of Monday, one-month (R 2 = 0.472) maturity IV was superior in predicting RV. Overall findings for the one-week horizon revealed that one-month maturity IV (R 2 = 0.472) in the closing period of Monday (begin-week day) held better predictive power when forecasting RV. For the one-month forecast horizon, in the opening period of Tuesday, two-month (R 2 = 0.386) maturity IV performed better when forecasting RV. In the midday period of Tuesday, two-month (R 2 = 0.332) maturity IV held higher predictive power when predicting RV. Finally, in the closing period of Tuesday, two-month (R 2 = 0.393) maturity IV was superior when predicting RV. Overall findings for the one-month horizon suggested that the two-month maturity IV (R 2 = 0.393) in the closing periods of Tuesday (begin-week day) held higher forecasting capabilities in predicting RV. The closing period IV better performed in forecasting RV for within-week, one-week, and one-month forecast horizons. Therefore, this study estimated the currency options price using IV based on options traded only during closing periods with a one-month, two-month, and three-month maturity. The closing period IV were used as inputs for the Equations (13) and (14) to estimate the call and put options model price, respectively. The MAE, MSE, and RMSE methods were employed in Equation (15), Equation (16) and Equation (17), respectively, to measure the options pricing error (OPE). Table 2describes the performance of IV to price the AUD options for the within-week forecast horizon, one-week forecast horizon, and one-month forecast horizon. J. Open Innov. Technol. Mark. Complex. 2021,7, 23 8 of 14 Table 1. Implied volatility (IV) forecast realised volatility (RV) for Australian dollar (AUD) options for within-week, one-week, and one-month forecast horizon. Time to Maturity Within-Week Forecast One-Week Forecast One-Month Forecast Mon to Fri Tue to Fri Wed to Fri Thu to Fri Mon to Mon Tue to Tue Wed to Wed Thu to Thu Fri to Fri Mon to Mon Tue to Tue Wed to Wed Thu to Thu Fri to Fri Panel A: Opening period (9:30−10:00) 1-month Slope 0.207 0.248 0.187 0.152 0.204 0.227 0.249 0.193 0.290 0.199 0.197 0.227 0.138 0.257 R20.133 0.19510.114 0.102 0.405 0.465 20.307 0.262 0.305 0.227 0.228 10.162 0.092 0.151 2-month Slope 0.415 0.479 0.483 0.443 0.366 0.414 0.504 0.445 0.445 0.324 0.337 0.449 0.357 0.361 R20.294 0.228 0.335 20.300 0.308 0.36510.321 0.342 0.238 0.356 0.386 20.263 0.217 0.177 3-month Slope 0.554 0.548 0.569 0.508 0.472 0.435 0.495 0.482 0.540 0.409 0.454 0.447 0.285 0.439 R20.221 0.336 20.288 0.270 0.253 0.284 10.161 0.183 0.212 0.249 0.295 10.162 0.202 0.170 Panel B: Midday period (12:30−13:00) 1-month Slope 0.248 0.245 0.207 0.253 0.216 0.217 0.227 0.310 0.260 0.194 0.196 0.205 0.215 0.224 R20.198 0.214 20.142 0.172 0.400 0.432 10.275 0.349 0.235 0.224 0.260 20.156 0.159 0.141 2-month Slope 0.427 0.411 0.390 0.425 0.364 0.353 0.397 0.436 0.390 0.304 0.317 0.364 0.347 0.290 R20.246 0.280 10.244 0.257 0.356 0.375 20.274 0.347 0.218 0.261 0.332 10.241 0.232 0.135 3-month Slope 0.470 0.486 0.465 0.479 0.396 0.419 0.473 0.513 0.479 0.332 0.385 0.413 0.415 0.362 R20.250 0.262 10.219 0.240 0.299 0.317 20.189 0.315 0.191 0.241 0.327 30.208 0.230 0.125 Panel C: Closing period (15:30−16:00) 1-month Slope 0.274 0.247 0.224 0.272 0.244 0.221 0.260 0.287 0.301 0.228 0.181 0.200 0.207 0.247 R20.313 30.207 0.160 0.213 0.472 3,*0.435 0.317 0.329 0.257 0.210 0.275 30.146 0.158 0.144 2-month Slope 0.432 0.427 0.426 0.458 0.378 0.380 0.423 0.430 0.434 0.320 0.322 0.353 0.350 0.325 R20.379 3,*0.273 0.252 0.294 0.39630.379 0.298 0.353 0.251 0.285 0.393 3,*0.215 0.248 0.158 3-month Slope 0.513 0.500 0.489 0.501 0.438 0.438 0.517 0.496 0.512 0.370 0.394 0.426 0.420 0.399 R20.352 30.258 0.248 0.292 0.335 30.310 0.240 0.290 0.228 0.284 0.310 20.207 0.238 0.146 Notes: IV represents implied volatility of Australian dollar (AUD) options. Equation (7) estimates IV using one-month (2 to 30 days), two-month (31 to 60 days), and three-month (61 to 90 days) maturity AUD options, for the opening (9:30 − 10:00), midday (12:30 − 13:00), and closing (15:30 − 16:00) a trading day. RV represents the realised volatility of Australian dollar. Equation (11) calculates the RV using the 5-min frequency AUD spot rate. The Mincer–Zarnowitz (MZ) regression analysis model, as in Equation (12), provides the slope coefficient and R 2 of within-week forecast horizon (Monday, Tuesday, Wednesday, and Thursday to Friday of the same week), one-week forecast horizon (Monday, Tuesday, Wednesday, Thursday, and Friday to Monday, Tuesday, Wednesday, Thursday, and Friday of next week, respectively), and one-month forecast horizon (Monday, Tuesday, Wednesday, Thursday, and Friday to Monday, Tuesday, Wednesday, Thursday, and Friday of next month, respectively) for the one-month, two-month, and three-month maturity options traded in the opening, midday, and closing of a trading day are given in panels A, B, and C, respectively. The p-value is zero for all cases and is not reported in the table to avoid repetition. Further, the zero p-values indicate that the null hypothesis is rejected at any level of significance. The superscripts 1, 2, and 3 denote the lower, mid, and higher value of R 2 , respectively, among different trading periods (opening, midday, closing) for the maturity of each option (one-month, two-month, three-month). The * represents the highest value of R 2 among one-month, two-month, and three-month maturity IV that lead the performance of IV to forecast RV for within-week, one-week, and one-month forecast horizon, respectively. Monday or Tuesday, Wednesday, and Thursday or Friday are considered as begin-week day, mid-week day, and end-week day, respectively.