Jump, Diffusion, and Long-Term Volatility Risks with Incremental Information in VIX Assets

Abstract

A reduced-form model is proposed to disentangle the dynamics of positive-jump, diffusion, and long-term risks in VIX assets. A dissection of the three component risks in volatility is undertaken to determine their distinctive dynamics, risk prices, and market information. The dynamics of three component volatility risks play important and distinctive roles in the VIX derivatives market. The risk dissection substantially improves VIX option valuation. The component risks considerably explain VIX asset returns with a distinct exposure pattern and require separate risk premia. The risks are priced distinctively in the volatility market and are sensitive to different macroeconomic conditions. A comparison of the VIX derivatives market with the S&P 500 market reveals incremental information from the component risks beyond that provided by the traditional S&P 500 and its option market. TOPICS:Derivatives, options, factors, risk premia Key Findings ▪ A reduced-form model is used to disentangle the jump risk dynamic from the diffusion and long-term risks in the volatility market. The dynamic volatility jump risk is shown to be critical in the VIX derivatives market. ▪ The authors find unique properties in the different volatility risks. The three component risks are separately priced in the VIX market, the risk premia compose the total variance premium by different patterns, and they have unique responding for the macroeconomic conditions. ▪ They compare the pricing information in the S&P 500 and volatility markets and show that component risk dynamics in the VIX derivatives market contain incremental and critical pricing information beyond what is embedded in the S&P 500 and its option market.