A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model |
| |
Authors: | Luca Vincenzo Ballestra Graziella Pacelli Francesco Zirilli |
| |
Affiliation: | 1. Dipartimento di Scienze Sociali “D. Serrani”, Università Politecnica delle Marche, Piazza Martelli 8, 60121 Ancona, Italy;2. Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy |
| |
Abstract: | We consider the problem of pricing European exotic path-dependent derivatives on an underlying described by the Heston stochastic volatility model. Lipton has found a closed form integral representation of the joint transition probability density function of underlying price and variance in the Heston model. We give a convenient numerical approximation of this formula and we use the obtained approximated transition probability density function to price discrete path-dependent options as discounted expectations. The expected value of the payoff is calculated evaluating an integral with the Monte Carlo method using a variance reduction technique based on a suitable approximation of the transition probability density function of the Heston model. As a test case, we evaluate the price of a discrete arithmetic average Asian option, when the average over n = 12 prices is considered, that is when the integral to evaluate is a 2n = 24 dimensional integral. We show that the method proposed is computationally efficient and gives accurate results. |
| |
Keywords: | G13 C63 |
本文献已被 ScienceDirect 等数据库收录! |
|