Overpriced Puts Puzzle in KOSPI 200 Options Market

Abstract

The purpose of this paper is to examine the argument that the put options traded in the exchanges are too high, compared to the asset prices based on the classical CAPM model, and thus the short position of the put option would make a significant profit from trading. In order to explore the earlier report, this paper, using the KOSPI 200 index options market price, estimates the historical rate of return on several option trading strategies such as naked option, protective put, covered call, straddle, and strangle. Secondly this paper compares the historical rates of return on the option trading strategies and Sharpe ratios with those generated by Monte-Carlo simulation and examines whether the historical option returns are inconsistent with Black-Scholes model, Jump-diffusion model, Stochastic Volatility model, or Stochastic Volatility with Jump model. Thirdly, this paper computes the optimal asset allocation ratio among the risk-free asset, risky assets, and option trading strategies in the viewpoint of rational investors who maximize the CRRA utility function. The results show that the historical returns on short position of ATM and OTM puts are too high to explain based on the classical CAPM, and the optimal allocation ratios among put, risky asset, and the risk-free asset are different from those derived using Monte-Carlo simulation.