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

Wang, Hengxu and O'Hara, John G and Constantinou, Nick (2015) 'A path-independent approach to integrated variance under the CEV model.' Mathematics and Computers in Simulation, 109. pp. 130-152. ISSN 0378-4754

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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.

Item Type: Article
Uncontrolled Keywords: CEV process; Realized variance; Small disturbance asymptotic expansion; Brownian bridge; Conditional Monte-Carlo simulation
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 02 Dec 2014 11:07
Last Modified: 15 Jan 2022 00:33

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