FX smile in the Heston model - Agnieszka Janek; Tino Kluge; Rafał Weron; Uwe Wystup (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2010)
The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options. In this article we adapt the original work of Heston (1993) to a foreign exchange (FX) setting. We discuss the computational aspects of using the semi-analytical formulas, performing Monte Carlo simulations, checking the Feller condition, and option pricing with FFT. In an empirical study we show that the smile of vanilla options can be reproduced by suitably calibrating three out of five model parameters.
Keywords: C5; C63; G13; 330; Heston model; vanilla option; stochastic volatility; Monte Carlo simulation; Feller condition; option pricing with FFT; Wechselkurs; Devisentermingeschäft; Optionspreistheorie; Volatilität; Stochastischer Prozess; Theorie