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On the equivalence of floating- and fixed-strike Asian options

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Vicky Henderson  and
Rafał Wojakowski
Vicky Henderson*
Affiliation:
University of Oxford
Rafał Wojakowski*
Affiliation:
Lancaster University
*
∗ Postal address: Nomura Centre for Quantitative Finance, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK. Email address: [email protected]
∗ Postal address: Department of Accounting and Finance, Lancaster University, Management School, Lancaster LA1 4YX, UK.
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Abstract

There are two types of Asian options in the financial markets which differ according to the role of the average price. We give a symmetry result between the floating- and fixed-strike Asian options. The proof involves a change of numéraire and time reversal of Brownian motion. Symmetries are very useful in option valuation, and in this case the result allows the use of more established fixed-strike pricing methods to price floating-strike Asian options.

Keywords

Asian optionfloating-strike Asian optionput call symmetrychange of numérairetime reversalBrownian motion

MSC classification

Primary: 60G44: Martingales with continuous parameter
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 391 - 394
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1] Alziary, B., Decamps, J. P., and Koehl, P. F. (1997). A PDE approach to Asian options: analytical and numerical evidence. J. Banking Finance 21, 613–640.CrossRefGoogle Scholar
[2] Bartels, H. J. (2000). On martingale diffusions describing the ‘smile effect’ for implied volatilities. Appl. Stoch. Models Business Industry 16, 1–10.3.0.CO;2-E>CrossRefGoogle Scholar
[3] Carr, P. and Schröder, M. (2000). On the valuation of arithmetic-average Asian options: the Geman–Yor Laplace transform revisited. Working Paper, Universität Mannheim.Google Scholar
[4] Chung, S. L., Shackleton, M., and Wojakowski, R. (2000). Efficient quadratic approximation of floating-strike Asian option values. Working paper, Lancaster University Management School.Google Scholar
[5] Donati-Martin, C., Ghomrasni, R., and Yor, M. (1999). On certain Markov processes attached to exponential functions of Brownian motion: applications to Asian options. Working paper, Université de Paris VI. Rev. Mat. Iberoamer. 17, 179–193.Google Scholar
[6] Dufresne, D. (2000). Laguerre series for Asian and other options. Math. Finance 10, 407–428.CrossRefGoogle Scholar
[7] Fu, M. C., Madan, D. B., and Wang, T. (1999). Pricing continuous Asian options: a comparision of Monte Carlo and Laplace transform inversion methods. J. Comput. Finance 2, 49–74.CrossRefGoogle Scholar
[8] Geman, H., El Karoui, N., and Rochet, J.-C. (1995). Changes of numéraire, changes of probability measure and option pricing. J. Appl. Prob. 32, 443–458.CrossRefGoogle Scholar
[9] Geman, H., and Yor, M. (1993). Bessel processes, Asian options and perpetuities. Math. Finance 3, 349–375.CrossRefGoogle Scholar
[10] Henderson, V., and Hobson, D. (2000). Local time, coupling and the passport option. Finance Stoch. 4, 69–80.CrossRefGoogle Scholar
[11] Kruizenga, R. J. (1964). Introduction to the option contract and profit returns from purchasing puts and calls. In The Random Character of Stock Market Prices, ed. Cootner, P. H., MIT Press, Cambridge, MA, pp. 337–391.Google Scholar
[12] Rogers, L. C. G., and Shi, Z. (1995). The value of an Asian option. J. Appl. Prob. 32, 1077–1088.CrossRefGoogle Scholar
[13] Vecer, J. (2001). A new PDE approach for pricing arithmetic Asian options. J. Comput. Finance 4, 105–113.CrossRefGoogle Scholar