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A Fitted Multi-point Flux Approximation Method for Pricing Two Options

Author

Listed:
  • Rock Stephane Koffi

    (The African Institute for Mathematical Sciences(AIMS)
    University of Cape Town)

  • Antoine Tambue

    (Western Norway University of Applied Sciences
    The African Institute for Mathematical Sciences(AIMS)
    University of Cape Town
    University of Cape Town)

Abstract

In this paper, we develop novel numerical methods based on the multi-point flux approximation (MPFA) method to solve the degenerated partial differential equation (PDE) arising from pricing two-assets options. The standard MPFA is used as our first method and is coupled with a fitted finite volume in our second method to handle the degeneracy of the PDE and the corresponding scheme is called fitted MPFA method. The convection part is discretized using the upwinding methods (first and second order) that we have derived on non uniform grids. The time discretization is performed with $$\theta $$θ-Euler methods. Numerical simulations show that our new schemes can be more accurate than the current fitted finite volume method proposed in the literature.

Suggested Citation

  • Rock Stephane Koffi & Antoine Tambue, 2020. "A Fitted Multi-point Flux Approximation Method for Pricing Two Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 597-628, February.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:2:d:10.1007_s10614-019-09906-x
    DOI: 10.1007/s10614-019-09906-x
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. 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.
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    Cited by:

    1. Sangkwon Kim & Jisang Lyu & Wonjin Lee & Eunchae Park & Hanbyeol Jang & Chaeyoung Lee & Junseok Kim, 2024. "A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2069-2086, May.
    2. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    3. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.

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