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

作者：Wang Hengxu; O'Hara John G^*; Constantinou Nick

来源：Mathematics and Computers in Simulation, 2015, 109: 130-152.

DOI：10.1016/j.matcom.2014.09.004

• CEV process
• Realized variance
• Small disturbance asymptotic expansion
• Brownian bridge
• Conditional Monte-Carlo simulation

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.

• 出版日期2015-3