Riccardo Brignone

Università degli Studi di Pavia

Title

Pricing path-dependent options under stochastic volatility models with full error control

Authors

Riccardo Brignone and Gero Junike

Abstract

In this paper, we propose a unified methodology for pricing general path-dependent derivatives (e.g., Asian and Barrier options), whose main benefit over existing literature consists in a simple and effective control of the error. A practitioner simply needs to provide to the pricing algorithm two parameters: i) a probability, $q$; ii) an error tolerance, $\epsilon$. Then, our proposed algorithm provides a price approximation that differs by no more than ε from the true unknown option price with probability at least equal to $q$. The proposed methodology works for a broad class of stochastic volatility models and it is based on the Monte Carlo-Conditional Fourier-cosine method. We provide an explicit link between the variance of the Monte Carlo simulation estimator of the option price, the error tolerance, and the number of simulations. In this way, the pricing methodology becomes extremely efficient when combined with effective variance reduction techniques that drastically reduce the number of simulations (and, therefore, the computing time) required to obtain an arbitrarily accurate price estimate.