Asian and Australian options: A common perspective
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).
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- repec:spr:compst:v:74:y:2011:i:1:p:93-120 is not listed on IDEAS
- Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
- Steven Vanduffel & Ales Ahcan & Luc Henrard & Mateusz Maj, 2012. "An Explicit Option-Based Strategy That Outperforms Dollar Cost Averaging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1250013-1-1.
- Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2095-2114, September.
- 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.
- 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.
- 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.
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- 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.
- Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
- Peter Carr & Christian-Oliver Ewald & Yajun Xiao, 2008.
"On the Qualitative Effect of Volatility and Duration on Prices of Asian Options,"
CRIEFF Discussion Papers
0803, Centre for Research into Industry, Enterprise, Finance and the Firm.
- 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.
- 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.
- 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.
- 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.
- 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.
- Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1001-1018. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.