Numerical Methods and Optimization in Finance

Chapter Fifteen

Calibrating Option Pricing Models

Publisher Summary

Option pricing models represent the price of the option as a function of the underlier; this underlier is then modeled usually via stochastic differential equations. Such differential equations require fixing certain parameters, for instance, the volatility of the underlier. Choosing such parameters is usually called calibration. Black–Scholes (BS) is the standard option-pricing model. Practitioners may not use it as it was intended, but it has become their language of choice. No other model will achieve this. In some products (for instance currencies), option prices are actually quoted in implied volatility. The success of the BS model stems not so much from its empirical quality, ...