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The value of an Asian option

Published online by Cambridge University Press:  14 July 2016

L. C. G. Rogers  and
Z. Shi
L. C. G. Rogers*
Affiliation:
Queen Mary and Westfield College, University of London
Z. Shi*
Affiliation:
Queen Mary and Westfield College, University of London
*
∗Present address: School of Mathematical Sciences, Claverton Down, Bath BA2 7AY, UK.
∗∗Present address: LSTA, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France.
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Abstract

This paper approaches the problem of computing the price of an Asian option in two different ways. Firstly, exploiting a scaling property, we reduce the problem to the problem of solving a parabolic PDE in two variables. Secondly, we provide a lower bound which is so accurate that it is essentially the true price.

Keywords

BROWNIAN MOTIONFIXED STRIKEFLOATING STRIKE
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1077 - 1088
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by SERC grant number GR/H 00444.

References

[1] Carverhill, A. P. and Clewlow, L. J. (1990) Flexible convolution. RISK April, 25–29.Google Scholar
[2] Curran, M. (1992) Beyond average intelligence. RISK November, 60.Google Scholar
[3] Geman, H. and Yor, M. (1992) Quelques relations entre processus de Bessel, options asiatiques, et fonctions confluentes hypergéométriques. C. R. Acad. Sci. Paris Série I314, 471–474.Google Scholar
[4] Geman, H. and Yor, M. (1993) Bessel processes, Asian options and perpetuities. Math. Finance 3, 349–375.Google Scholar
[5] Ingersoll, J. E. (1987) Theory of Financial Decision Making. Blackwell, Oxford.Google Scholar
[6] Kemna, A. G. Z. and Vorst, A. C. F. (1990) A pricing method for options based on average asset values. J. Banking Finan. March, 113–129.CrossRefGoogle Scholar
[7] Levy, E. (1990) Asian arithmetic. RISK May, 7–8.Google Scholar
[8] Levy, E. (1992) Pricing European average rate currency options. J. Internat. Money Finan. 11, 474–491.Google Scholar
[9] Levy, E. and Turnbull, S. (1992) Average intelligence. RISK February, 5–9.Google Scholar
[10] Ruttiens, A. (1990) Classical replica. RISK February, 33–36.Google Scholar
[11] Turnbull, S. M. and Wakeman, L. M. (1991) A quick algorithm for pricing European average options. J. Financial Quantitative Anal., 377–389.Google Scholar
[12] Vorst, A. C. F. (1990) Analytic boundaries and approximations of the prices and hedge ratios of average exchange rate options. Unpublished manuscript, Econometric Institute, Erasmus University, Rotterdam.Google Scholar
[13] Yor, M. (1992) On some exponential functionals of Brownian motion. Adv. Appl. Prob. 24, 509–531.CrossRefGoogle Scholar