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

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

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Abstract

© 2014 International Association for Mathematics and Computers in Simulation (IMACS). 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
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Nick Constantinou
Date Deposited: 02 Dec 2014 11:07
Last Modified: 03 Sep 2019 02:15
URI: http://repository.essex.ac.uk/id/eprint/11941

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