Black-Scholes Approximations of Call Option Prices with Stochastic Volatilities: A Note

A piecewise linear weighting function for Black-Scholes implied volatilities is used in conjunction with the Black-Scholes call pricing model to approximate stochastic volatility European call prices. A sensitivity analysis is conducted to compare simulated stochastic volatility call prices to the Black-Scholes prices calculated with the weighted implied volatilities. The analysis indicates that a simple model can provide close approximations to the simulated prices with far less computational effort.