Price and Volatility Dynamics Implied by the VIX Term Structure

A particle-filter based estimation method is developed for the stochastic volatility model with/without jumps and applied on the S&P 500 index value and the VIX term structure jointly. The model encompasses all mean-reverting stochastic volatility option pricing models with a constant elasticity of variance, and can allow for price jumps. Our contention is that using the VIX term structure in estimation can help reach a more reliable conclusion on the nature of the risk-neutral volatility dynamic. Our empirical findings are: (1) the volatility process under the risk-neutral measure is mean-reverting; (2) the jump intensity is time-varying; (3) the jump and volatility risks are priced; (4) the measurement errors in VIXs are material; and (5) the square-root volatility process is mis-specified with or without price jumps. JEL classification code: G12, G13. ∗Duan is with Risk Management Institute and Business School, National University of Singapore. E-mail: [email protected]. Yeh is with Department of Finance, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung, Taiwan. Email: [email protected]. The authors thank the participants of the 4th Annual the Society for Financial Econometrics Conference for valuable comments. Price and Volatility Dynamics Implied by the VIX Term Structure