The concern of this article is to specify the stochastic process of KOSPI 200 and to price the options based on the specified process. The Generalized Method of Moments (GMM) was used to estimate the Constant Elasticity of Variance (CEV) parameter and to test the structural change in stochastic process. Throughout the estimation and test procedures, it is found that the unrestricted CEV model was the model appropriately describing the KOSPI200 process. It was also found that the structural change of the processes took place during the currency crisis and IMF bailout program in Korea. The CEV parameter changed from 0.06 in the pre-IMF period to 0.87 in the post-IMF period. At the same time, the volatility of return of KOSPI200 has doubled during the IMF bailout program.
Using the estimated process, I calculated the prices of options on KOSPI200 and compared them with market prices. The Finite Difference Method (FDM) was used as a numerical approach to compute theoretical option prices based on the process. The results show that both the prices based on the estimated CEV process and lognormal process were slightly higher than market prices. Although the theoretical prices based on CEV and the lognormal process show pricing errors, the former outperformed the latter in terms of Mean Squared Error (MSE).
