Option pricing : different approaches to black-Scholes and Heston models with empirical tests.

Abstract

In the past four decades, derivative markets have become increasingly important in the world of finance and investment. Various financial models have been introduced with the development of modern option pricing system. Among them, Black-Scholes model and Heston model are, perhaps, two of the most widely recognized methods for valuing options.

Although plenty of previous studies have been done to analyze and test these two models, this research area still deserves further investigation. The purpose of our study is to find different but simpler approaches to derive Black-Scholes model and Heston model, respectively. The report elaborates on Wiener Process and Itô’s Lemma, the foundation for derivation of Black-Scholes model, before utilizing an easier method to derive this model. Moreover, in terms of stochastic volatility, self-financing and Itô’s Lemma, a different derivation to Heston Partial Differential Equation is developed, where market price of volatility risk is deduced at the same time. In addition, empirical tests with data from Standard & Poor's 500 index options are launched to compare the effectiveness of two models, in recent volatile options market after European debt crisis. The experimental results conclude that Heston model fits the market better than Black-Scholes model. Finally, this report discusses the implications of these two models and provides new insights into derivatives pricing system.