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Pricing American-Style Derivatives with European Call Options

Author

Listed:
  • Scott B. Laprise

    (BAE Systems, Advanced Information Technologies, 3811 N. Fairfax Drive, Arlington, Virginia 22203)

  • Michael C. Fu

    (The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

  • Steven I. Marcus

    (Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742)

  • Andrew E. B. Lim

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

  • Huiju Zhang

    (The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

Abstract

We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to the pricing of a portfolio of European call options, leading to analytical expressions for those cases where analytical European call prices are available (e.g., the Merton jump-diffusion process). Furthermore, in many settings, the approach yields upper and lower analytical bounds that provably converge to the true option price. We provide computational results to illustrate the convergence and accuracy of the resulting estimators.

Suggested Citation

  • Scott B. Laprise & Michael C. Fu & Steven I. Marcus & Andrew E. B. Lim & Huiju Zhang, 2006. "Pricing American-Style Derivatives with European Call Options," Management Science, INFORMS, vol. 52(1), pages 95-110, January.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:1:p:95-110
    DOI: 10.1287/mnsc.1050.0447
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    References listed on IDEAS

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    Cited by:

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    2. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    3. Rojas-Bernal, Alejandro & Villamizar-Villegas, Mauricio, 2021. "Pricing the exotic: Path-dependent American options with stochastic barriers," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 2(1).
    4. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    5. Zhang, Xiaoyuan & Zhang, Tianqi, 2023. "On pricing double-barrier options with Markov regime switching," Finance Research Letters, Elsevier, vol. 51(C).
    6. Geoffrey Poitras & Chris Veld & Yuriy Zabolotnyuk, 2009. "European Put-Call Parity and the Early Exercise Premium for American Currency Options," Multinational Finance Journal, Multinational Finance Journal, vol. 13(1-2), pages 39-54, March-Jun.
    7. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    8. Weiping Li & Su Chen, 2018. "The Early Exercise Premium In American Options By Using Nonparametric Regressions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-29, November.

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