FOURTH-ORDER COMPACT SCHEME FOR OPTION PRICING UNDER THE MERTON’S AND KOU’S JUMP-DIFFUSION MODELS

Kuldip Singh Patel () and Mani Mehra ()
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Kuldip Singh Patel: Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India
Mani Mehra: Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 04, 1-26

Abstract: In this paper, a compact scheme with three time levels is proposed to solve the partial integro-differential equation that governs the option prices in jump-diffusion models. In the proposed compact scheme, the second derivative approximation of the unknowns is approximated using the value of these unknowns and their first derivative approximations, thereby allowing us to obtain a tridiagonal system of linear equations for a fully discrete problem. Moreover, the consistency and stability of the proposed compact scheme are proved. Owing to the low regularity of typical initial conditions, a smoothing operator is employed to ensure the fourth-order convergence rate. Numerical illustrations concerning the pricing of European options under the Merton’s and Kou’s jump-diffusion models are presented to validate the theoretical results.

Keywords: Compact schemes; option pricing; Lévy process; European options; jump-diffusion models; partial integro-differential equations; Toeplitz matrices (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024918500279

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