(An) empirical investigation of price behavior in option markets

Abstract

This thesis focuses on empirical investigation on implied volatility, which is an important issue to practitioners and also researchers in the option markets. The empirical investigation can be divided into two categories. One is based on the tree model that is a discrete version of variables and other is based on the closed-form solution that is continuous version of variables. In the former half part of this thesis, implied tree models is introduced and compared for KOSPI 200 index options with regards to the pricing and hedging performance. With Cox, Ross and Rubinstein``s (1979) standard binomial tree (SBT) model as a benchmark, three models- Rubinstein``s (1994) implied binomial tree (IBT), Jackwerth``s (1997) generalized binomial tree (GBT), and Derman and Kani``s (1994) implied volatility tree (IVT) models, is analyzed. The SBT model, the simplest, shows the best performance. Moreover, the delta-hedged strategy in all of the binomial models generates, on average, negative gains. This finding, consistent with the findings by Bakshi and Kapadia (2003), indicates the existence of a negative market volatility risk premium. In the latter half part of this thesis, a closed-form solution is presented for the valuation of European options under the assumption that the excess returns of the underlying asset follow a diffusion process. In light of this formula, the implied volatility computed from Black-Scholes formula should be viewed as the volatility of excess returns rather than of gross returns. Though Black-Scholes formula is nested in this formula, analyses using SPX, and OMX options data do not provide strong evidences indicating that empirical implications are significantly better than those of Black-Scholes formula due to insignificant difference between the volatilities of gross returns and excess returns.