Valuation of an option using non-parametric methods

Abstract

This paper provides a general valuation model to fairly price a European option using parametric and non-parametric methods. In particular, we show how to use the historical simulation (HS) method, a well-known non-parametric statistical method applied in the financial area, to price an option. The advantage of the HS method is that one can directly obtain the distribution of stock returns from historical market data. Thus, it not only does a good job in capturing any characteristics of the return distribution, such as clustering and fat tails, but it also eliminates the model errors created by mis-specifying the distribution of underlying assets. To solve the problem of measuring transformation in valuing options, we use the Esscher’s transform to convert the physical probability measure to the forward probability measure. Taiwanese put and call options are used to illustrate the application of this method. To clearly show which model prices stock options most accurately, we compare the pricing errors from the HS method with those from the Black–Scholes (BS) model. The results show that the HS model is more accurate than the BS model, regardless for call or put options. More importantly, because there is no complex mathematical theory underlying the HS method, it can easily be applied in practice and help market participants manage complicated portfolios effectively.