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A moving boundary approach to American option pricing

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  • Muthuraman, Kumar

Abstract

This paper describes a method to solve the free-boundary problem that arises in the pricing of American options. Most numerical methods for American option pricing exploit the representation of the option price as the expected pay-off under the risk-neutral measure and calculate the price for a given time to expiration and stock price. They do not solve the related free-boundary problem explicitly. The advantage of solving the free-boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly. Our approach, which we term the Moving Boundary Approach, is based on using a boundary guess and the value associated with the guess to construct an improved boundary. It is also shown that on iteration, the sequence of boundaries converge monotonically to the optimal exercise boundary. Examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented. Finally, we compare runtimes and speeds with other methods that solve the free-boundary problem and compute the optimal boundaries explicitly, like the front-fixing method, penalty method, method based on the integral representations and the method by Brennan and Schwartz [1977. The valuation of American put options. Journal of Finance 32 (2), 449-462].

Suggested Citation

  • Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:11:p:3520-3537
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    References listed on IDEAS

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    Cited by:

    1. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    2. repec:eee:dyncon:v:80:y:2017:i:c:p:75-100 is not listed on IDEAS
    3. Chockalingam, Arun & Feng, Haolin, 2015. "The implication of missing the optimal-exercise time of an American option," European Journal of Operational Research, Elsevier, vol. 243(3), pages 883-896.
    4. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
    5. Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    6. Zhu, Song-Ping & Chen, Wen-Ting, 2013. "An inverse finite element method for pricing American options," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 231-250.

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