Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T21:17:00.770Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL

Part of: Mathematical finance

Published online by Cambridge University Press:  27 January 2016

SANAE RUJIVAN
SANAE RUJIVAN*
Affiliation:
Division of Mathematics and Statistics, School of Science, Walailak University, Nakhon Si Thammarat 80161, Thailand email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

Keywords

gamma swapsweighted variance swapsHeston modelstochastic volatility

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 244 - 268
Copyright
© 2016 Australian Mathematical Society 

References

Broadie, M. and Jain, A., “The effect of jumps and discrete sampling on volatility and variance swaps”, Int. J. Theor. Appl. Finance 11 (2008) 761–797; doi:10.1142/S0219024908005032.Google Scholar
Brzeźniak, Z. and Zastawniak, T., Basic stochastic processes, Springer Undergraduate Mathematics Series (Springer-Verlag, London, 1999).CrossRefGoogle Scholar
Cox, J. C., Ingersoll, J. E. Jr and Ross, S. A., “A theory of the term structure of interest rates”, Econometrica 53 (1985) 385–407; http://econpapers.repec.org/article/ecmemetrp/v_3a53_3ay_3a1985_3ai_3a2_3ap_3a385-407.htm.CrossRefGoogle Scholar
Crosby, J., “Exact pricing of discretely-sampled variance derivatives”, J. Bus. Manag. Appl. Econom. 2 (2013) 1–24; http://journals.indexcopernicus.com/abstract.php?icid=1100887.Google Scholar
Heston, S. L., “A closed-form solution for options with stochastic volatility with applications to bond and currency options”, Rev. Financ. Stud. 6 (1993) 327–343; doi:10.1093/rfs/6.2.327.CrossRefGoogle Scholar
Mougeot, N., Volatility investing handbook (BNP Paribas, Paris, 2005);http://quantlabs.net/academy/download/free_quant_instituitional_books_/[BNP%20Paribas]%20Volatility%20Investing%20Handbook.pdf.Google Scholar
Øksendal, B., Stochastic differential equations (Springer, Berlin, 2003).CrossRefGoogle Scholar
Overhaus, M., Bermudez, A., Buehler, H., Ferraris, A., Jordinson, C. and Lamnouar, A., Equity hybrid derivatives (Wiley & Sons, Hoboken, NJ, 2007).Google Scholar
Rujivan, S. and Zhu, S.-P., “A simplified analytical approach for pricing discretely-sampled variance swaps with stochastic volatility”, Appl. Math. Lett. 25 (2012) 1644–1650; doi:10.1016/j.aml.2012.01.029.Google Scholar
Rujivan, S. and Zhu, S.-P., “A simple closed-form formula for pricing discretely-sampled variance swaps under the Heston model”, ANZIAM J. 56 (2014) 1–27; doi:10.1017/S1446181114000236.Google Scholar
Yuen, C. and Kwok, Y., “Pricing exotic variance swaps under 3/2-stochastic volatility models”, working paper, 2014, https://www.math.ust.hk/people/faculty/maykwok/piblications/.Google Scholar
Zheng, W. and Kwok, Y., “Closed form pricing formulas for discretely sampled generalized variance swaps”, Math. Finance 24 (2014) 855–881; doi:10.1111/mafi.12016.CrossRefGoogle Scholar
Zhu, S.-P. and Lian, G., “On the valuation of variance swaps with stochastic volatility”, Appl. Math. Comput. 219 (2012) 1654–1669; doi:10.1016/j.amc.2012.08.006.Google Scholar