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Asian and Australian options: A common perspective

Author

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  • Ewald, Christian-Oliver
  • Menkens, Olaf
  • Hung Marten Ting, Sai

Abstract

We show that Australian options are equivalent to fixed or floating strike Asian options and consequently that by studying Asian options from the Australian perspective and vice versa, much can be gained. One specific application of this “Australian approach” leads to a natural dimension reduction for the pricing PDE of Asian options, with or without stochastic volatility, featuring time independent coefficients. Another application lies in the improvement of Monte Carlo schemes, where the “Australian approach” results in a path-independent method. We also show how the Milevsky and Posner (1998) result on the reciprocal Γ-approximation for Asian options can be quickly obtained by using the connection to Australian options. Further, we present an analytical (exact) pricing formula for Australian options and adapt a result of Carr et al. (2008) to show that the price of an Australian call option is increasing in the volatility and by doing this answering a standing question by Moreno and Navas (2008).

Suggested Citation

  • Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1001-1018
    DOI: 10.1016/j.jedc.2013.01.006
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    References listed on IDEAS

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    1. Jacques, Michel, 1996. "On the Hedging Portfolio of Asian Options," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(02), pages 165-183, November.
    2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
    3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    4. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
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    6. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
    7. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
    8. Martzoukos, Spiros H., 2001. "The option on n assets with exchange rate and exercise price risk," Journal of Multinational Financial Management, Elsevier, vol. 11(1), pages 1-15, February.
    9. Yang, Zhaojun & Ewald, Christian-Oliver, 2010. "On the non-equilibrium density of geometric mean reversion," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 608-611, April.
    10. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    11. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    12. repec:spr:compst:v:74:y:2011:i:1:p:93-120 is not listed on IDEAS
    13. Griselda Deelstra & Freddy Delbaen, 1998. "Convergence of discretised stochastic interest rate: processes with stochastic drift term," ULB Institutional Repository 2013/7584, ULB -- Universite Libre de Bruxelles.
    14. Constantinides, George M., 1979. "A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(02), pages 443-450, June.
    15. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    16. Carr, Peter & Ewald, Christian-Oliver & Xiao, Yajun, 2008. "On the qualitative effect of volatility and duration on prices of Asian options," Finance Research Letters, Elsevier, vol. 5(3), pages 162-171, September.
    17. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
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    1. repec:wsi:rpbfmp:v:20:y:2017:i:01:n:s0219091517500059 is not listed on IDEAS
    2. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    3. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    4. Ewald, Christian-Oliver & Yor, Marc, 2015. "On increasing risk, inequality and poverty measures: Peacocks, lyrebirds and exotic options," Journal of Economic Dynamics and Control, Elsevier, vol. 59(C), pages 22-36.

    More about this item

    Keywords

    Asset pricing; Derivatives; Asian options; Quanto options; Dollar cost averaging (DCA); Numerical methods;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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