Pricing Variance Swap by Estimating Risk Neutral Density

• Activity Number: 426
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Liyuan Jiang* and Keren Li and Fangfang Wang and Jie Yang
• Companies: and University of Illinois at Chicago and University of Illinois at Chicago and University of Illinois at Chicago
• Keywords: Financial statistics ; Risk management ; Hyperbolic distribution ; Risk neutral measure ; Variance swap ; Variance future

Abstract

We aim to price variance swap, a novel over-the-counter (OTC) financial contract that allows investors to hedge risks due to the volatility of some underlying financial product. We derive the theoretical price of variance swap under no-arbitrage assumption. Based on the vanilla option prices traded on the Chicago Board Options Exchange (CBOE), we are able to estimate the moments of the risk neutral density under a fairly general theoretical framework. We develop a calibration approach to estimate the fair price of variance swap using the moments estimated. In order to compare our theoretical price with the marketing price of variance swap, we create the historical price of variance swap from the corresponding CBOE variance future market prices. We evaluate our approach using the variance future market prices obtained from CBOE.