Binomial Option Pricing Biases and Inconsistent Implied Volatilities

We evaluate the binomial option pricing methodology (OPM) by examining simulated portfolio strategies. A key aspect of our study involves sampling from the empirical distribution of observed equity returns. Using a Monte Carlo simulation, we generate equity prices under known volatility and return parameters. We price American–style put options on the equity and evaluate the risk–adjusted performance of various strategies that require writing put options with different maturities and moneyness characteristics. The performance of these strategies is compared to an alternative strategy of investing in the underlying equity. The relative performance of the strategies allows us to identify biases in the binomial OPM leading to the well–known volatility smile. By adjusting option prices so as to rule out dominated option strategies in a mean–variance context, we are able to reduce the pricing errors of the OPM with respect to option prices obtained from the LIFFE. Our results suggest that a simple recalibration of inputs may improve binomial OPM performance.