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.

A numerical method to price exotic path dependent options on an underlying described by the Heston stochastic volatility model / L. V., Ballestra; G., Pacelli; Zirilli, Francesco. - In: JOURNAL OF BANKING & FINANCE. - ISSN 0378-4266. - 31:(2007), pp. 3420-3437. [10.1016/j.jbankfin.2007.04.013]

A numerical method to price exotic path dependent options on an underlying described by the Heston stochastic volatility model

ZIRILLI, Francesco
2007

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.
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A numerical method to price exotic path dependent options on an underlying described by the Heston stochastic volatility model / L. V., Ballestra; G., Pacelli; Zirilli, Francesco. - In: JOURNAL OF BANKING & FINANCE. - ISSN 0378-4266. - 31:(2007), pp. 3420-3437. [10.1016/j.jbankfin.2007.04.013]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1378
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