Simulation of L&#233vy-Driven models and its application in finance

Rachel Chen; Jianqiang Hu; Yijie Peng

doi:10.3934/naco.2012.2.749

Article Contents

2012, Volume 2, Issue 4: 749-765. Doi: 10.3934/naco.2012.2.749

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Simulation of Lévy-Driven models and its application in finance

1.
School of Management, Fudan University, Guoshun Road 670, Shanghai 200433

Received: May 2012

Revised: September 2012

Published: October 2012

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Abstract

Lévy processes have been widely used to model financial assets such as stock prices, exchange rates, interest rates, and commodities. However, when applied to derivative pricing, very few analytical results are available except for European options. Therefore, one usually has to resort to numerical methods such as Monte Carlo simulation method. The simulation method is attractive in that it is very general and can also handle high dimensional problems very well. In this survey paper, we provide an overview on various simulation methods for Lévy processes. In addition, we introduce two simulation based sensitivity estimation methods: perturbation analysis and the likelihood ratio method. Sensitivity estimation is useful in various applications, such as derivative pricing and parameter estimation. Finally, we provide a simple illustrative example of applying simulation and sensitivity estimation to parameter estimation of Lévy-driven stochastic volatility model.

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Mathematics Subject Classification: Primary: 60G05, 68U20.

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