Monte Carlo Pricing of Derivative Securities and Uncertainty in Volatility Estimation

Abstract

In the standard time-inhomogeneous di usion model, estimation of the volatility function is far more important for Monte Carlo pricing than estimation of the drift function (due to a standard application of Girsanov's Theorem). As such, we study the distribution of option prices under the uncertainty of volatility function estimation. First, we run Monte Carlo simulations to price a variety of options using a xed estimate of the volatility function. Then, we run Monte Carlo simulations to price a variety of options using a bootstrapped re-estimation of volatility function in each Monte Carlo trial. The di erences in the resulting distributions of option prices may have implications for thinking about the bid-ask spread on an option price, and can be compared to historical data to gain a more complete perspective on the acceptability of various American-style option prices.