Volatility estimation by combining stock price data and option data

Volatility modeling and analysis are traditionally based on either historical price data or option data. Finance theory shows that option prices heavily depend on the under-lying stocks' prices, thus the two kinds of data are related. This paper explores the approach that combines both stock price data and option data to perform the statistical analysis of volatility. We investigate the Black-Scholes model and an exponential GARCH model and derive the relationship among the Fisher information for volatility estimation based on stock price data alone or option data alone as well as joint volatility estimation for combining stock price data and option data. Under the Black-Scholes model an asymptotic theory for the joint estimation is established, and a simulation study is conducted to check finite sample performances of the proposed joint estimation.