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Bounds for in-progress floating-strike Asian options using symmetry

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Abstract

This paper studies symmetries between fixed and floating-strike Asian options and exploits this symmetry to derive an upper bound for the price of a floating-strike Asian. This bound only involves fixed-strike Asians and vanillas, and can be computed simply given one of the many efficient methods for pricing fixed-strike Asian options. The bound coincides with the true price until after the averaging has begun and again at maturity. The bound is compared to benchmark prices obtained via Monte Carlo simulation in numerical examples.

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References

  • Bouaziz, L., E. Briys, and M. Crouhy. (1994). “The Pricing of Forward-Starting Asian Options.” Journal of Banking and Finance, 18, 823–839.

    Article  Google Scholar 

  • Carr, P. and M. Schröder. (2000). “On the Valuation of Arithmetic-Average Asian Options: The Geman-Yor Laplace Transform Revisited.” Universität Mannheim working paper.

  • Chung, S.L., M. Shackleton, and R. Wojakowski. (2003). “Efficient Quadratic Approximation of Floating Strike Asian Option Values.” Revue Finance, 24(1).

  • Conze, A. and Visvanathan. (1991). “European Path Dependent Options: The Case of Geometric Averages.” Finance, 12(1), 7–22.

    Google Scholar 

  • Corwin, J., P. Boyle, and K. Tan. (1996). “Quasi Monte Carlo Method in Numerical Finance.” Management Science, 42, 926–938.

    Google Scholar 

  • Curran, M. (1994). “Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price.” Management Science, 40(12), 1705–1711.

    Google Scholar 

  • Donati-Martin, C., R. Ghomrasni, and M. Yor. (2001). “On certain Markov Processes Attached to Exponential Functions of Brownian Motion: Applications to Asian Options.” Revista Matematica Iberoamericana, 17, 179–193.

    Google Scholar 

  • Dufresne, D. (1990). “The Distribution of a Perpetuity with Applications to Risk Theory and Pension Funding.” Scandinavian Actuarial Journal, 39–79.

  • Eberlein, E. and A. Papapantoleon. (2005). “Equivalence of Floating and Fixed Strike Asian and Lookback Options.” Stochastic Processes and Their Applications, 115, 31–40.

    Article  Google Scholar 

  • Fu, M.C., D.B. Madan, and T. Wang. (1999). “Pricing Continuous Asian Options: A Comparision of Monte Carlo and Laplace Tranform Inversion Methods.” Journal of Computational Finance, 2(2), 49–74.

    Google Scholar 

  • Geman, H. and M. Yor. (1993). “Bessel Processes, Asian Options and Perpetuities.” Mathematical Finance, 3(4), 349–375.

    Article  Google Scholar 

  • Henderson, V. and R. Wojakowski. (2002). “On the Equivalence of Fixed and Floating-Strike Asian Options.” Journal of Applied Probability, 39(2), 391–394.

    Article  Google Scholar 

  • Hoogland, J.K and C.D.D. Neumann. (2000). “Asians and Cash Dividends: Exploiting Symmetries in Pricing Theory.” Preprint, CWI, The Netherlands.

  • Ingersoll, J. (1987). “Theory of Financial Decision Making.” Rowman and Littlefield.

  • Linetsky, V. (2004). “Spectral Expansions for Asian (Average Price) Options.” Operations Research, 52, 856–867.

    Article  Google Scholar 

  • Marcozzi, M.D. (2003). “On the Valuation of Asian Options by Variational Methods.” SIAM Journal of Scientific Computing, 24(4), 1124–1140.

    Article  Google Scholar 

  • Matsumoto, M. and T. Nishimura. (1998). “Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudorandom Number Generator.” ACM Transcations on Modeling and Computer Simulation, 8(1), 3–30.

    Article  Google Scholar 

  • Nielsen, J.A. and K. Sandmann. (2003). “Pricing Bounds on Asian Options.” Journal of Financial and Quantitative Analysis, 38(2).

  • Ritchken, P., L. Sankarasubramanian, and A.M. Vijh. (1993). “The Valuation of Path Dependent Contracts on the Average.” Management Science, 39(10), 1202–1213.

    Article  Google Scholar 

  • Rogers, L.C.G. and Shi, Z. (1995). “The Value of An Asian Option.” Journal of Applied Probability, 32(4), 1077–1088.

    Article  Google Scholar 

  • Schröder, M. (2002). “On the Valuation of Arithmetic-Average Asian Options: Laguerre Series and Theta Integrals.” Universität Mannheim working paper.

  • Shaw, W.T. (2000). “A Reply to Pricing Continuous Asian Options by Fu, Madan and Wang.” Working Paper.

  • Shaw, W.T. (2002). “Accurate Pricing of Asian Options by Contour Integration Including Efficient Methods for Low Volatility.” Working Paper.

  • Vanmaele, M., G. Deelstra, J. Liinev, J. Dhaene, and M.J. Goovaerts. (2005). “Bounds for the Price of Discretely Sampled Arithemetic Asian Options.” To appear in Journal of Computational and Applied Mathematics.

  • Vecer, J. (2001). “A New PDE Approach for Pricing Arithmetic Asian Options.” Journal of Computational Finance, 4(4), 105–113.

    Google Scholar 

  • Vecer, J. (2002). “Unified Asian Pricing.” RISK, June, pp. 113–116.

  • Vyncke, D., M. Goovaerts, and J. Dhaene. (2003). “An Accurate Analytical Approximation for the Price of a European-Style Arithmetic Asian Option.” Proceedings of the Seventh International Congress on Insurance: Mathematics and Economics, Lyon.

  • Yor, M. (2001). “Exponential Functionals of Brownian Motion and Related Processes.” New York: Springer-Verlag.

    Google Scholar 

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Correspondence to Vicky Henderson.

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D. Hobson is supported by an Advanced Fellowship from the EPSRC.

V. Henderson is partially supported by the NSF under grant DMI 0447990.

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Henderson, V., Hobson, D., Shaw, W. et al. Bounds for in-progress floating-strike Asian options using symmetry. Ann Oper Res 151, 81–98 (2007). https://doi.org/10.1007/s10479-006-0122-8

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