Instantaneous Squared VIX and VIX Derivatives （瞬时平方波动率指数和波动率指数衍生品）.pdf

Instantaneous Squared VIX and VIX Derivatives Xingguo Luo and Jin E. Zhang† This version: August 22, 2014 Abstract In this paper, we provide a unified theoretical framework to price VIX derivatives, including futures and options written on both VIX and VXST. Our theory is built on Luo and Zhang’s (2012) concept of instantaneous squared VIX (ISVIX) that is the sum of instantaneous Brownian and jump variances of SPX return. Modeling ISVIX as a mean- reverting jump-diffusion process with a stochastic long-term mean, we obtain analytical formulas for the prices of VIX options and futures. Calibration with the market data of VIX option implied volatility surface shows that our theory provides an efficient way of extracting the complete information from VIX derivatives market for the dynamics of underlying SPX. Keywords: VIX; VXST; Instantaneous squared VIX; VIX futures; VIX option JEL Classification Code: C2; C13; G13; †Xingguo Luo is from College of Economics and Academy of Financial Research, Zhejiang University, Hangzhou 310027, PR China. Email: xingguoluo@, and Jin E. Zhang is from Department of Accountancy and Finance, Otago Business School, University of Otago, Dunedin 9054, New Zealand. Email: jin.zhang@otago.ac.nz. Instantaneous squared VIX and VIX Derivatives 1 Instantaneous Squared VIX and VIX Derivatives Abstract In this paper, we provide a unified theoretical framework to price VIX derivatives, including futures and options written on both VIX and VXST. Our theory is built on Luo and Zhang’s (2012) concept of instantaneous squared VIX (ISVIX) that is the sum of