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Approximate valuation of average options

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Abstract

This paper concerns the valuation of average options of European type where an investor has the right to buy the average of an asset price process over some time interval, as the terminal price, at a prespecified exercise price. A discrete model is first constructed and a recurrence formula is derived for the exact price of the discrete average call option. For the continuous average call option price, we derive some approximations and theoretical upper and lower bounds. These approximations are shown to be very accurate for at-the-money and in-the-money cases compared to the simulation results. The theoretical bounds can be used to provide useful information in pricing average options.

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Author notes

  1. Toshihiro Yoshida

    Present address: Salomon Brothers Asia Limited, 2-2-2 Otemachi, Chiyoda-ku, 100, Tokyo, Japan

  2. Hideki Iwaki

    Present address: Department of Management, Faculty of Business Administration, Nanzan University, 18 Yamasato-cho, Showa-ku, 466, Nagoya, Japan

Authors and Affiliations

  1. Graduate School of Commerce, Hitotsubashi University, 2-1, Naka, 186, Kunitachi-city, Tokyo, Japan

    Hideki Iwaki

  2. Graduate School of Systems Management, The University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 112, Tokyo, Japan

    Masaaki Kijima

Authors
  1. Hideki Iwaki
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  2. Masaaki Kijima
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  3. Toshihiro Yoshida
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Iwaki, H., Kijima, M. & Yoshida, T. Approximate valuation of average options. Ann Oper Res 45, 131–145 (1993). https://doi.org/10.1007/BF02282045

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