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General Lower Bounds for Arithmetic Asian Option Prices

Listed author(s):
  • H. Albrecher
  • P. A. Mayer
  • W. Schoutens
Registered author(s):

    This paper provides model-independent lower bounds for prices of arithmetic Asian options expressed through prices of European call options on the same underlying that are assumed to be observable in the market, and the corresponding subreplicating strategy is identified. The first bound relies on the no-arbitrage assumption only and turns out to perform satisfactorily in various situations. It is shown how the bound can be tightened under mild additional assumptions on the underlying market model. This considerably generalizes lower bounds in the literature, which are only available in the Black-Scholes world. Furthermore, it is illustrated how to adapt the procedure to the case where only a finite number of strikes is available in the market. As a by-product, the finite strike upper bound on the Asian call price of Hobson et al. (2005a), who considered basket options, is rederived. Numerical illustrations of the bounds are given together with comparisons to bounds resulting from model specifications.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13527260701356633
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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 15 (2008)
    Issue (Month): 2 ()
    Pages: 123-149

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    Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:123-149
    DOI: 10.1080/13527260701356633
    Contact details of provider: Web page: http://www.tandfonline.com/RAMF20

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    5. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
    6. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
    7. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
    8. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    9. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    10. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    11. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    12. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    13. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
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