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Sensitivity analysis of the early exercise boundary for American style of Asian options

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  • Daniel Sevcovic
  • Martin Takac

Abstract

In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying asset prices over some predetermined time interval. The mathematical model for the option price leads to a free boundary problem for a parabolic partial differential equation. Applying fixed domain transformation and transformation of variables we develop an efficient numerical algorithm based on a solution to a non-local parabolic partial differential equation for the transformed variable representing the synthesized portfolio. For various types of averaging methods we investigate the dependence of the early exercise boundary on model parameters.

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  • Daniel Sevcovic & Martin Takac, 2011. "Sensitivity analysis of the early exercise boundary for American style of Asian options," Papers 1101.3071, arXiv.org.
    • Handle: RePEc:arx:papers:1101.3071
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    References listed on IDEAS

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    1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    2. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893.
    3. Geske, Robert & Roll, Richard, 1984. "On Valuing American Call Options with the Black-Scholes European Formula," Journal of Finance, American Finance Association, vol. 39(2), pages 443-455, June.
    4. Daniel Sevcovic, 2008. "Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black-Scholes equations," Papers 0805.0611, arXiv.org.
    5. Tomas Bokes & Daniel Sevcovic, 2009. "Early exercise boundary for American type of floating strike Asian option and its numerical approximation," Papers 0912.1321, arXiv.org.
    6. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
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    8. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82, January.
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