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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, Cambridge University Press, vol. 26(2), pages 165-183, November.
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    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(3), 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.
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    Citations

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    Cited by:

    1. Jilong Chen & Christian Ewald, 2017. "On the Performance of the Comonotonicity Approach for Pricing Asian Options in Some Benchmark Models from Equities and Commodities," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-32, March.
    2. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    3. Jan Vecer, 2013. "Asian options on the harmonic average," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1315-1322, September.
    4. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    5. 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.
    6. 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.
    7. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.

    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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