Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models

Abstract

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the implied volatility of stocks derived from traded call and put options prices compared to historical volatility estimates sourced from IVolatility.com (“IVolatility”). Our evidence suggests use of the Bayesian approach to estimate volatility can provide a more accurate measure of ex-ante stock price volatility and will be useful in the pricing of derivative securities where the implied stock price volatility cannot be observed.