Calibration Design of Implied Volatility Surfaces

Abstract

The calibration of option pricing models leads to the minimization of an error functional. We show that its usual specification as a root mean squared error implies fluctuating exotics prices and possibly wrong prices. We propose a simple and natural method to overcome these problems, illustrate drawbacks of the usual approach and show advantages of our method. To this end, we calibrate the Heston model to a time series of DAX implied volatility surfaces and then price cliquet options.

Implied Volatility Surface: Construction Methodologies and Characteristics

“…In various flavors it was shown to outperform all other global optimization algorithms when solving benchmark problems (unconstrained, bounded or constrained optimization). Various papers and presentations described successful calibrations done with Differential Evolution in finance: [26,27,54,142,40], to mention but a few.…”