การประเมินมูลค่าออปชันบนดัชนีเอสแอนด์พี 500 โดยใช้แบบจำลอง เฮสตันด้วยพารามิเตอร์จากวิธีภาวะน่าจะเป็นสูงสุด

Abstract

The Black-Scholes model (1973) is one of the most popular financial models for options pricing under -measure or the risk-neutral world. However, this model has been criticised about the pricing accuracy because the model assumptions are strictly. This cause in the development of other stochastic models. Heston model (1993) is a stochastic model which relaxes the constant volatility assumption and options pricing can be obtained in semi-closed form. The assumption of Heston model is that the underlying asset price has the volatility which varies on time which the behaviour of the volatility follows the Cox-Ingersoll-Ross model. This implies that there are 2 sources of risk, price risk and volatility risk. Moreover, in order to price the option, we must change the measure of Heston model to -measure which Heston (1993) recommended function for the sources of risk to substituting in an adapted process. In this work, we have found a condition for changing measure of the Heston model. It turns out that recommended the function by Heston is only one of infinite possible choices of this model. Consequently, the relationship between the market price of volatility risk and degree of risk aversion in the market is studied when the isoelastic utility function is issued the price. Finally, we use data of the S&P 500 Index and applying theory of Aït-Sahalia (2008) to estimate parameters of the Black-Scholes model and the Heston model, then compare these 2 models to find out which model is better for pricing options compare to the actual prices.