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Option pricing in jump diffusion models with quadratic spline collocation

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  • Christara, Christina C.
  • Leung, Nat Chun-Ho

Abstract

In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, the pricing problem can be solved efficiently. We present the method and the numerical results from pricing European and American options with Merton’s and Kou’s models.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:279:y:2016:i:c:p:28-42
    DOI: 10.1016/j.amc.2015.12.045
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    References listed on IDEAS

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    Cited by:

    1. Georgiev, Slavi G. & Vulkov, Lubin G., 2021. "Computation of the unknown volatility from integral option price observations in jump–diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 591-608.
    2. 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.
    3. Deswal, Komal & Kumar, Devendra, 2022. "Rannacher time-marching with orthogonal spline collocation method for retrieving the discontinuous behavior of hedging parameters," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Jan Posp'iv{s}il & Vladim'ir v{S}v'igler, 2019. "Isogeometric analysis in option pricing," Papers 1910.00258, arXiv.org.

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