Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T11:32:47.224Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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