A Linear Regression Approach for Determining Explicit Expressions for Option Prices for Equity Option Pricing Models with Dependent Volatility and Return Processes

Abstract

We consider a risk-neutral stock-price model where the volatility and the return processes are assumed to be dependent. The market is complete and arbitrage-free. Using a linear regression approach, explicit functions of risk-neutral density functions of stock return functions are obtained and closed form solutions of the corresponding Black-Scholes-type option pricing results are derived. Implied volatility skewness properties are illustrated.