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

Author

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  • 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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