Complexity reduction for calibration to American options

Olena Burkovska, Kathrin Glau, Mirco Mahlstedt and Barbara Wohlmuth

Abstract

American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to their higher flexibility compared with European options, the mathematical model involves additional constraints, and a variational inequality is obtained. We use the Heston stochastic volatility model to describe the price of a single stock option. In order to speed up the calibration process, we apply two model-reduction strategies. First, we introduce a reduced basis method. We thereby reduce the computational complexity of solving the parametric partial differential equation drastically, compared with a classical finite-element method, which makes applications of standard minimization algorithms for the calibration significantly faster.