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Approximating payoffs and pricing formulas

Author

Listed:
  • Serge Darolles

    (DRM-Finance - DRM - Dauphine Recherches en Management - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Paul Laurent

    (Financial models, Group ALM - BNP Paribas, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We use the ideas developed by Madan and Milne (1994. Mathematical Finance 3, 223-245), Lacoste (1996. Mathematical Finance 6, 197-213) to explore the optimality of polynomial approximations in pricing securities. In particular, we look at the approximations for security payoffs as well as the associated pricing formula in a L2 framework. We apply these ideas to two examples, one where the state variable follows an Ornstein-Uhlenbeck process and one based on Brownian motion with reflecting barriers, to illustrate the strengths and weaknesses of the approach.

Suggested Citation

  • Serge Darolles & Jean-Paul Laurent, 2000. "Approximating payoffs and pricing formulas," Post-Print halshs-00678228, HAL.
    • Handle: RePEc:hal:journl:halshs-00678228
    DOI: 10.1016/S0165-1889(99)00092-5
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    Citations

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    Cited by:

    1. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.
    2. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    3. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    4. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.

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