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A Variable Reduction Technique for Pricing Average-Rate Options

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  • Hua He and Akihiko Takahashi.

Abstract

Average-rate options, commonly known as Asian options, are contingent claims whose payoffs depend on the arithmetic average of some underlying index over a fixed time horizon. This paper proposes a new valuation technique, called the variable reduction technique, for average rate options. This method transforms the valuation problem of an average-rate option into an evaluation of a conditional expectation that is determined by a one-dimensional Markov process (as opposed to a two-dimensional Markov process). This variable reduction technique works directly with the arithmetic average and does not encounter approximation errors when volatility of the underlying is relatively large. Further, reducing the dimensionality by one makes pricing more efficient in terms of computing time. The variable reduction technique is applied in a simple Black-Scholes' economy in which there is one risky asset and one riskless bond. The paper also discusses application of the technique to average-rate options where the underlying index is an interest rate. Numerical comparisons of different methods are also presented.

Suggested Citation

  • Hua He and Akihiko Takahashi., 1995. "A Variable Reduction Technique for Pricing Average-Rate Options," Research Program in Finance Working Papers RPF-249, University of California at Berkeley.
  • Handle: RePEc:ucb:calbrf:rpf-249
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    Cited by:

    1. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian Options," Working Papers 28, Barcelona School of Economics.
    2. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    3. Kenji Kamizono & Takeaki Kariya & Regina Liu & Teruo Nakatsuma, 2004. "A New Control Variate Estimator for an Asian Option," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(2), pages 143-160, June.

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