Getting the Right Option Price with the Wrong Model
15 Pages Posted: 13 Oct 2001
Date Written: October 8, 2001
Despite recent advances in modeling option prices, traders and other practitioners have resisted using more complex theoretical formulas. The most widely used valuation procedure among practitioners is a variant of the Black-Scholes framework with ad hoc adjustments and frequent updating. Why do traders continue to use this practitioner Black-Scholes (PBS) model to price and hedge options when the model's assumptions about the underlying asset price are clearly wrong? In this paper, we provide a theoretical justification for the practice. We show that the PBS model can be cast as a functional approximation to the true but unknown option pricing formula. When fit to a large number of observed prices, the implied volatility surface will exactly price the full cross-section. If the implied volatility surface is re-calibrated sufficiently frequently, then out of sample forecasts of option prices become arbitrarily accurate.
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