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

• Published in: Mathematics and computers in simulation Vol. 109; pp. 130 - 152
• Main Authors: Wang, Hengxu, O’Hara, John G., Constantinou, Nick
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2015
• Subjects: Brownian bridge; CEV process; Conditional Monte-Carlo simulation; Realized variance; Small disturbance asymptotic expansion; Small disturbance asymptotic expansion; CEV process; Realized variance; Conditional Monte-Carlo simulation; Brownian bridge
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2014.09.004

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.