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The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach
- Source :
- Computers & Mathematics with Applications. 60:1571-1590
- Publication Year :
- 2010
- Publisher :
- Elsevier BV, 2010.
-
Abstract
- We consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is described by a jump-diffusion stochastic differential equation in which the jump term consists of a Lvy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. Pricing American options under the Bates model requires us to solve a partial integro-differential equation with the final condition and boundary conditions prescribed on a free boundary. In this paper a numerical method for solving such a problem is proposed. In particular, first of all, using a Richardson extrapolation technique, the problem is reduced to a problem with fixed boundary. Then the problem obtained is solved using an ad hoc finite element method which efficiently combines an implicit/explicit time stepping, an operator splitting technique, and a non-uniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is extremely accurate and fast. In particular it is significantly more efficient than other numerical methods that have recently been proposed for pricing American options under the Bates model. © 2010 Elsevier Ltd. All rights reserved.
- Subjects :
- Mathematical optimization
Stochastic volatility
Option pricing
Lvy processe
Finite elements
Richardson extrapolation
Trinomial tree
Finite element method
Computational Mathematics
Stochastic differential equation
Finite element
Computational Theory and Mathematics
Lévy processes
Valuation of options
Modelling and Simulation
Computational Theory and Mathematic
Modeling and Simulation
Binomial options pricing model
Boundary value problem
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 60
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....a0758be9f7a73063af3fab10da1a6852