Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options

In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).