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A path-independent approach to integrated variance under the CEV model

Author

Listed:
  • Wang, Hengxu
  • O’Hara, John G.
  • Constantinou, Nick

Abstract

In this paper, a closed form path-independent approximation of the fair variance strike for a variance swap under the constant elasticity of variance (CEV) model is obtained by applying the small disturbance asymptotic expansion. The realized variance is sampled continuously in a risk-neutral market environment. With the application of a Brownian bridge, we derive a theorem for the conditionally expected product of a Brownian motion at two different times for arbitrary powers. This theorem enables us to provide a conditional Monte-Carlo scheme for simulating the fair variance strike. Compared with results in the recent literature, the method outlined in our paper leads to a simplified approach for pricing variance swaps. The method may also be applied to other more sophisticated volatility derivatives. An empirical comparison of this model with the Heston model and a conditional Monte Carlo scheme is also presented using option data on the S&P 500.

Suggested Citation

  • Wang, Hengxu & O’Hara, John G. & Constantinou, Nick, 2015. "A path-independent approach to integrated variance under the CEV model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 130-152.
    • Handle: RePEc:eee:matcom:v:109:y:2015:i:c:p:130-152
    DOI: 10.1016/j.matcom.2014.09.004
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    References listed on IDEAS

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    1. Mark Broadie & Ashish Jain, 2008. "The Effect Of Jumps And Discrete Sampling On Volatility And Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 761-797.
    2. Lindsay, A.E. & Brecher, D.R., 2012. "Simulation of the CEV process and the local martingale property," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 868-878.
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    6. Richard Jordan & Charles Tier, 2009. "The Variance Swap Contract Under The Cev Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 709-743.
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