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Valuing American options by simulation: A BSDEs approach

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  • Klimsiak, Tomasz
  • Rozkosz, Andrzej
  • Ziemkiewicz, Bartosz

Abstract

We provide probabilistic proofs of convergence of several easy to implement schemes for computing the value function of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. The proofs are based on representations of the value function by means of solutions of some backward stochastic differential equations. Despite the probabilistic nature of the proofs the numerical schemes are nevertheless deterministic. Simulation results are also presented.

Suggested Citation

  • Klimsiak, Tomasz & Rozkosz, Andrzej & Ziemkiewicz, Bartosz, 2016. "Valuing American options by simulation: A BSDEs approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 123(C), pages 1-18.
    • Handle: RePEc:eee:matcom:v:123:y:2016:i:c:p:1-18
    DOI: 10.1016/j.matcom.2015.11.009
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
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    Cited by:

    1. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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