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Annals of Operations Research

, Volume 45, Issue 1, pp 131–145 | Cite as

Approximate valuation of average options

  • Hideki Iwaki
  • Masaaki Kijima
  • Toshihiro Yoshida
Article
  • 39 Downloads

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.

Keywords

Average (Asian) option discrete model Black-Scholes equation option pricing 

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References

  1. [1]
    F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81 (1973) 637–659.Google Scholar
  2. [2]
    A.P. Carverhill and L.J. Clewlow, Valuing average rate (“Asian”) options, Risk 3 (1990) 25–29.Google Scholar
  3. [3]
    J.C. Cox, S. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Fin. Econ. 7 (1979) 229–263.Google Scholar
  4. [4]
    H. Geman and M. Yor, Bessel processes, Asian options and other applications, Working paper (1992).Google Scholar
  5. [5]
    J. Hull,Options, Futures, and Other Derivative Securities (Prentice-Hall, 1989).Google Scholar
  6. [6]
    J. Hull and A. White, The use of the control variate technique in option pricing, J. Fin. Quan. Anal. 23 (1988) 237–251.Google Scholar
  7. [7]
    A.G.Z. Kemna and A.C.F. Vorst, A pricing method for options based on average asset values, J. Banking Fin. 14 (1990) 113–129.Google Scholar
  8. [8]
    E. Lévy, Pricing European average rate currency options, J. Int. Money Fin. (1991), to appear.Google Scholar
  9. [9]
    A.C.F. Vorst, Average rate exchange options, Erasmus University working paper (1990).Google Scholar
  10. [10]
    D. Stoyan,Comparison Methods for Queues and Other Stochastic Models (Wiley, 1983).Google Scholar
  11. [11]
    M. Yor, On some exponential functions of Brownian motion, Adv. Appl. Prob. 24 (1992) 509–531.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Hideki Iwaki
    • 1
  • Masaaki Kijima
    • 2
  • Toshihiro Yoshida
    • 3
  1. 1.Graduate School of CommerceHitotsubashi UniversityKunitachi-city, TokyoJapan
  2. 2.Graduate School of Systems ManagementThe University of TsukubaTokyoJapan
  3. 3.Salomon Brothers Asia LimitedTokyoJapan

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