IMEX Methods for Pricing Fixed Strike Asian Options with Jump-Diffusion Models
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In this paper we study implicit-explicit(IMEX)methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian op- tion is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order conver- gence rate.
Abstract
In this paper we study implicit-explicit(IMEX)methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian op- tion is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order conver- gence rate.
참고문헌 (10)
- B. Alziary, "A P.D.E. approach to Asian options:analytical and numerical evidence", J. Bank Financ, 21, pp.613~640 (1997)
- E. Bayraktar, "Pricing Asian options for jump diffiusion", Math. Financ, 21, pp.117~143 (2011)
- Z. Cen, "Finite diffierence scheme with a moving mesh for pricing Asian options", Appl. Math. Comput, 219, pp.8667~8675 (2013)
- P. A. Forsyth, "Convergence of numerical methods for valuing path-dependent options using interpolation", Rev. Deriv. Res, 5, pp.273~314 (2002)
- Y. d'Halluin, "A semi-Lagrangian approach for Amer-ican Asian options under jump diffiusion", SIAM J. Sci. Comput., 27, pp.315~345 (2005)
- J. Hugger, "Wellposedness of the boundary value formulation of a fixed strike Asian option", J. Comput. Appl. Math, 185, pp.460~481 (2006)
- D. Y. Tangman, "Fast simplified approaches to Asian option pricing", J. Comput. Financ, 14, pp.3~36 (2011)
- J. Vecer, "A new PDE approach for pricing arithmetic average Asian options", J. Com-put. Financ, 4, pp.105~113 (2001)
- B. Zhang, "Efficient pricing of European-style Asian options under exponential Levy processes based on Fourier cosine expansions", SIAM J. Financ. Math, 4, pp.399~426 (2013)
- R. Zvan, "Robust numerical methods for PDE models of Asian options", J. Comput. Financ, 1, pp.39~78 (1997)