Chapter 17 - Calibrating option pricing models

Abstract

We explain how to calibrate the parameters of option pricing models so that these models fit given market prices. We start with the Black–Scholes case in which we need just one parameter (implied volatility); then we move to models that require to set several parameters. For such models, calibration often leads to optimization problems that cannot be solved with standard methods, hence we use heuristics (Differential Evolution and Particle Swarm Optimization). We investigate several examples, like Heston's stochastic volatility model or Bates' model which includes jumps. We show how to price options under these models using the characteristic function, and how to calibrate the parameters of the models with heuristic techniques. Along the way we give a brief introduction to numerical integration and explain Newton–Cotes and Gauss rules. Sample code is provided.