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

  • Vicky Henderson (a1) and Rafał Wojakowski (a2)
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.

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Corresponding author
Postal address: Nomura Centre for Quantitative Finance, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK. Email address: henders1@maths.ox.ac.uk
Postal address: Department of Accounting and Finance, Lancaster University, Management School, Lancaster LA1 4YX, UK.
References
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[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, 613640.
[2] Bartels, H. J. (2000). On martingale diffusions describing the ‘smile effect’ for implied volatilities. Appl. Stoch. Models Business Industry 16, 110.
[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.
[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.
[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, 179193.
[6] Dufresne, D. (2000). Laguerre series for Asian and other options. Math. Finance 10, 407428.
[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, 4974.
[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, 443458.
[9] Geman, H., and Yor, M. (1993). Bessel processes, Asian options and perpetuities. Math. Finance 3, 349375.
[10] Henderson, V., and Hobson, D. (2000). Local time, coupling and the passport option. Finance Stoch. 4, 6980.
[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. 337391.
[12] Rogers, L. C. G., and Shi, Z. (1995). The value of an Asian option. J. Appl. Prob. 32, 10771088.
[13] Vecer, J. (2001). A new PDE approach for pricing arithmetic Asian options. J. Comput. Finance 4, 105113.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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