An Empirical Test of the Hull-White Option Pricing Model

The Black-Scholes (1973) option pricing model provides the foundation for the modern theory of options valuation. In actual applications, however, the model has certain well-known deficiencies. For example, when calibrated to accurately price at-the-money options the Black-Scholes (1973) model often misprices deep in-the-money and deep out-of-themoney options. This model-anomalous behavior gives rise to what options professionals call “volatility smiles.” A volatility smile is the skewed pattern that results from calculating implied volatilities across a range of strike prices for an option series. This phenomenon is not predicted by the Black-Scholes (1973) model, since volatility is a property of the underlying instrument and the same implied volatility value should be observed across all options on that instrument. Volatility smiles are generally thought to result from the parsimonious assumptions used to derive the Black-Scholes model. In particular, the Black-Scholes (1973) model assumes that security log prices follow a constant variance diffusion process. The constant variance assumption has been tested and rejected in early studies by Beckers (1980), Black and Scholes (1972), Christie