Hobson, David and Klimmek, Martin. (2012) Model-independent hedging strategies for variance swaps. Finance and Stochastics, Vol.16 (No.4). pp. 611-649. ISSN 0949-2984

Text WRAP_Hobson_varswap.pdf - Accepted Version Restricted to Repository staff only until 1 November 2013. Download (2010Kb)

Abstract

A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths, it is well known that the variance swap payoff can be replicated exactly using a portfolio of puts and calls and a dynamic position in the asset. This fact forms the basis of the VIX contract. But what if we are in the more realistic setting where the contract is based on discrete monitoring, and the underlying asset may have jumps? We show that it is possible to derive model-independent, no-arbitrage bounds on the price of the variance swap, and corresponding sub- and super-replicating strategies. Further, we characterise the optimal bounds. The form of the hedges depends crucially on the kernel used to define the variance swap.

Item Type:	Journal Article
Subjects:	H Social Sciences > HG Finance
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Derivative securities -- Econometric models, Hedging (Finance) -- Econometric models
Journal or Publication Title:	Finance and Stochastics
Publisher:	Springer
ISSN:	0949-2984
Date:	October 2012
Volume:	Vol.16
Number:	No.4
Page Range:	pp. 611-649
Identification Number:	10.1007/s00780-012-0190-3
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
References:	[1] J. Azema and M. Yor. Une solution simple au probleme de Skorokhod. In Seminaire de Probabilites, XIII (Univ. Strasbourg, Strasbourg, 1977/78), volume 721 of Lecture Notes in Math., pages 90–115. Springer, Berlin, 1979. [2] A. Bick and W. Willinger. Dynamic spanning without probabilities. Stochastic Processes and their Aplications, 50:349–374, 1994. [3] O. Bondarenko. Variance trading and market price of variance risk. Working paper, 2007. [4] D.T. Breeden and R.H. Litzenberger. Prices of state-contingent claims implicit in option prices. J. Business, 51:621–651, 1978. [5] M. Broadie and A. Jain. The effect of jumps and discrete sampling on volatility and variance swaps. Int. J. of Th. and App. Finance, 11(8):761–791, 2008. [6] H. Brown, D.G. Hobson, and L.C.G Rogers. Robust hedging of barrier options. Math. Finance, 11(3):285–314, 2001. [7] P. Carr and A. Corso. Covariance contracting for commodities. Energy and Power Risk Management, April:42–45, 2001. [8] P. Carr and R. Lee. Variation and share-weighted variation swaps on time-changed L´evy processes. Preprint, 2010. [9] P. Carr, R. Lee, and L. Wu. Variance swaps on time-changed L´evy processes. Preprint, 2010. [10] A. Cox and J. Wang. Root’s barrier: construction, optimality and applications to variance options. Preprint, 2011. [11] M.H.A. Davis and D.G. Hobson. The range of traded option prices. Mathematical Finance, 17(1):1–14, 2007. [12] K. Demeterfi, E. Derman, M. Kamal, and J. Zou. A guide to volatility and variance swaps. The Journal of Derivatives, 6(4):9–32, 1999. [13] K. Demeterfi, E. Derman, M. Kamal, and J. Zou. More than you ever wanted to know about volatility swaps. Goldman-Sachs Quantitive Strategies Research Notes, 1999. [14] L.E. Dubins and D. Gilat. On the distribution of maxima of martingales. Proceedings of the American Mathematical Society, 68:337–338, 1978. [15] B. Dupire. Arbitrage pricing with stochastic volatility. Societe Generale, Options Division, Paris, 1992. [16] H. F¨ollmer. Calcul d’Ito sans probabilites. In S´eminaire de Probabilites, XV (Univ. Strasbourg, Strasbourg, 1981), volume 850 of Lecture Notes in Math., pages 143–150. Springer, Berlin, 1981. [17] D.G Hobson. Robust hedging of the lookback option. Finance and Stochastics, 2:329–347, 1998. [18] D.G. Hobson. The Skorokhod embedding problem and model independent bounds for option prices. In Paris-Princeton Lecture Notes on Mathematical Finance. Springer, 2010. [19] D.G. Hobson and M. Klimmek. Maximising functionals of the joint law of the maximum and terminal value in the Skorokohd embedding problem. Preprint, 2010. [20] D.G. Hobson and J. L. Pedersen. The minimum maximum of a continuous martingale with given initial and terminal laws. Ann. Probab., 30(2):978–999, 2002. [21] R. Jarrow, Y. Kchia, M. Larsson, and P. Protter. Discretely sampled variance and volatility swaps versus their continuous approximations. Preprint, 2011. [22] N. Kahal´e. Model-independent lower bound on variance swaps. Preprint, 2011. [23] I. Martin. Simple variance swaps. Preprint, 2011. [24] A. Neuberger. The Log Contract. Journal of Portfolio Management, 20(2):74–80, 1994. [25] A. Neuberger. Realized skewness. Working paper, 2010. [26] E. Perkins. The Cereteli-Davis solution to the H1-embedding problem and an optimal embedding in Brownian motion. In Seminar on Stochastic Processes, 1985 (Gainesville, Fla., 1985), pages 172–223. Birkhauser Boston, Boston, MA, 1986. [27] A. V. Skorokhod. Studies in the theory of random processes. Translated from the Russian by Scripta Technica, Inc. Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. [28] S. Zhu and G-H. Lian. A closed-form exact solution for pricing variance swaps with stochastic volatility. Mathematical Finance, 21(2):233–256, 2011.
URI:	http://wrap.warwick.ac.uk/id/eprint/50314

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item