Why Simulations Are an Unreliable Test of Option Strategies

Abstract

* Since the start of listed options trading in 1973, computer simulations have become increasingly popular as a method for testing and comparing option strategies. Simulations can typically answer the question, Given the actual history of security prices, what return on investment would a given options strategy have produced? But they cannot reveal whether a specific option strategy is good, bad or indifferent. To do this, a test must maintain between the options strategies compared. The key to stock equivalence is the neutral hedge ratio the rate at which option prices change with changes in underlying stock prices. The neutral hedge ratio changes with changes in the ratio of striking price to market price, in the time remaining to expiration and in the volatility of the underlying stock. Such well known simulations as those of Kassouf and Merton, Scholes and Gladstein rely on test portfolios with fixed positions, neglecting the fact that the stock equivalence of those positions will vary over time. The sophisticated investor is less interested in the hypothetical return on investment from a particular option strategy than with its probable impact on the risk-reward structure of his current portfolio. The authors propose an index approach that is specifically designed to answer the latter question. It assesses option strategies by comparing actual and implied stock price volatilities. If the volatility implied by the option price as traded exceeds the stock's actual volatility, the price of the option has exceeded its value. >