Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options

Purpose: Recently, considerable attention has been given to forecasting, not only the mean and the variance, but also the entire probability density function (pdf) of the underlying asset. These forecasts can be obtained as implied moments of future distribution originating from European call and put options. However, the predictive accuracy of option pricing models is not so well established. With this in mind, this research aims to identify the model that predicts the entire pdf most accurately when compared to the ex-post “true” density given by high-frequency data at expiration date. Methodology: The methodological part includes two steps. In the first step, several probability density functions are estimated using different option pricing models, considering the values of major market indices with different maturities. These implied probability density functions are risk neutral. In the second step, the implied pdfs are compared against the “true” density obtained from the high-frequency data to examine which one gives the best fit out-of-sample. Results: The results support the idea that a “true” density function, although unknown, can be estimated by employing the kernel estimator within high-frequency data and adjusted for risk preferences. Conclusion: The main conclusion is that the Shimko model outperforms the Mixture Log-Normal model as well as the Edgeworth expansion model in terms of out-of-sample forecasting accuracy. This study contributes to the existing body of research by: i) establishing the benchmark of the “true” density function using high-frequency data, ii) determining the predictive accuracy of the option pricing models and iii) providing applicative results both for market participants and public authorities.

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Efficiency of S&P CNX Nifty Index Option of the National Stock Exchange (NSE), India, using Box Spread Arbitrage Strategy

Gadjah Mada International Journal of Business ◽

10.22146/gamaijb.5473 ◽

2014 ◽

Vol 15 (3) ◽

pp. 269 ◽

Cited By ~ 2

Author(s):

G. P. Girish ◽

Nikhil Rastogi

Keyword(s):

High Frequency ◽

Stock Exchange ◽

Estimation Error ◽

High Frequency Data ◽

Frequency Data ◽

Index Options ◽

Time Period ◽

Arbitrage Strategy ◽

Computational Simplicity ◽

Index Option

Box spread is a trading strategy in which one simultaneously buys and sells options having the same underlying asset and time to expiration, but different exercise prices. This study examined the efficiency of European style S&P CNX Nifty Index options of National Stock Exchange, (NSE) India by making use of high-frequency data on put and call options written on Nifty (Time-stamped transactions data) for the time period between 1st January 2002 and 31st December 2005 using box-spread arbitrage strategy. The advantages of box-spreads include reduced joint hypothesis problem since there is no consideration of pricing model or market equilibrium, no consideration of inter-market non-synchronicity since trading box spreads involve only one market, computational simplicity with less chances of mis-specification error, estimation error and the fact that buying and selling box spreads more or less replicates risk-free lending and borrowing. One thousand three hundreds and fifty eight exercisable box-spreads were found for the time period considered of which 78 Box spreads were found to be profitable after incorporating transaction costs (32 profitable box spreads were identified for the year 2002, 19 in 2003, 14 in 2004 and 13 in 2005) The results of our study suggest that internal option market efficiency has improved over the years for S&P CNX Nifty Index options of NSE India.

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