Analysis and pricing of call option with the heston model

Abstract

Black-Scholes model is an option theory published by collected papers of university of Chicago at 1973. They derived Black-Scholes formula using five parameters: current stock price, volatility, time to expire, strike price and interest rate. Since there was no organized option theory, Black-Scholes model contributed greatly to the extension of trading volume with sensation. So far, it has been widely used as typical option theory. However Black-Scholes model has some weaknesses ; They assumed that a volatility is constant, and ignored a dividend and so on. Because of these reasons, movements to find more suitable model for the real market has being active. One of the results of movement is stochastic volatility model which solved constant volatility problem. The most famous stochastic volatility model is the Heston model introduced at 1993 by Heston. The purpose of this paper is that to analyze the Heston model and to suggest some useful tips when you use the Heston model. Among the all options, we will focus on a European call option especially. Indeed we can easily compute European put option price from put-call parity if we know European call price.