The impact of estimation errors on the option pricing

The Normal Inverse Gaussian distribution is used as a model of logarithmic returns of index values. We use the Esscher transform and the Black Scholes formula for the option pricing. The calibration of the distribution parameters afects the calculated prices of the European call options. The basic idea is to use a point estimation and its standard errors and then test combinations when the standard errors are added or subtracted to the point estimates. The study is applied to two indexes of the OMX Nordic Market, the OMXS30 and OMXC20. Our results on these indexes show that the parameter which influences the option price mostly is the peakeness of the NIG distribution. The skewness parameter has the least influence on the pricing. The option prices based on the NIG and Esscher transform are also compared with the pricing by using Black-Scholes formula and the market prices. The results show that for the OMXS30 index the NIG assumption and the Esscher transform provide calculated prices which are closer to the market prices that the Black-Scholes prices. For the OMXC20 we obtained contrary results.