Implied volatility with transaction costs and the market efficiency of the KOSPI 200 option market

Abstract

The “smile” in Black-Scholes implied volatilities is observed in KOSPI 200 index option market. And the Black-Scholes implied volatility is not an unbiased estimator of the future realized volatility over the remaining life of the option. These anomalies cannot be explained in the pure Black-Scholes economy. The possible explanations are: 1) The underlying asset’s return process is not a geometric Brownian motion process, 2) transaction costs and the measurement errors in variable exist, and/or 3) the market is inefficient. This paper examines the possibility that the measurement errors in variables and the transaction costs cause the anomalies. Empirical results show that the measurement errors and transaction costs may explain the volatility “smile”, but cannot explain the bias of implied volatilities, especially for the ATM options, in forecasting the future realized volatility. We also examine whether the trading strategy of selling the overvalued and buying the undervalued by Black-Scholes formula, brings profits to investors. This strategy with delta-neutral hedging generates substantial pre-transaction cost trading profits. This strategy still remains profitable even after considering the transaction costs. This trading profits support the market inefficiency. Some other evidence showing the possibility of the market inefficiency is suggested in the paper.