Tweaking Black-Scholes

Abstract

Option professionals routinely tweak the Black-Scholes option pricing model using a volatility smile. Using algebraic analysis and Monte Carlo simulation experiments, we compare the hedging performance of the tweaked Black-Scholes option pricing model with a stochastic volatility model in a stochastic volatility setting. We find that the tweaked Black-Scholes model almost perfectly mimics the stochastic volatility model representing the true stochastic process. This suggests why volatility smiles are widely used by options professionals to calibrate option trading and hedging strategies. These results also have implications for empirical tests of option pricing models.

Keywords: options, hedging, Black-Scholes

JEL Classification: G12, G13