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Efficient pricing of options in jump–diffusion models: Novel implicit–explicit methods for numerical valuation

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  • Maurya, Vikas
  • Singh, Ankit
  • Yadav, Vivek S.
  • Rajpoot, Manoj K.

Abstract

This paper presents novel implicit–explicit Runge–Kutta type methods for numerically simulating partial integro-differential equations that arise when pricing options under jump–diffusion models. These methods offer an alternative approach that avoids the need for numerical or analytical inversion of the coefficient matrix. The pricing of European options is formulated as a partial integro-differential equation, while the pricing of American options are treated as a linear complementarity problem. The developed implicit–explicit Runge–Kutta type method is combined with an operator splitting technique to efficiently solve the linear complementarity problem. Stability and convergence analysis of the proposed methods are established using discrete ℓ2-norm. To validate their efficiency and accuracy, the methods are applied to pricing European and American options under Merton’s and Kou’s models, and the computed results are compared with those reported in the literature.

Suggested Citation

  • Maurya, Vikas & Singh, Ankit & Yadav, Vivek S. & Rajpoot, Manoj K., 2024. "Efficient pricing of options in jump–diffusion models: Novel implicit–explicit methods for numerical valuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 202-225.
    • Handle: RePEc:eee:matcom:v:217:y:2024:i:c:p:202-225
    DOI: 10.1016/j.matcom.2023.10.025
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    References listed on IDEAS

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    1. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    2. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    3. Christara, Christina C. & Leung, Nat Chun-Ho, 2016. "Option pricing in jump diffusion models with quadratic spline collocation," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 28-42.
    4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Yadav, Vivek S. & Ganta, Naveen & Mahato, Bikash & Rajpoot, Manoj K. & Bhumkar, Yogesh G., 2022. "New time-marching methods for compressible Navier-Stokes equations with applications to aeroacoustics problems," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    8. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    9. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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