The Price of Higher Order Catastrophe Insurance: The Case of VIX Options
150 Pages Posted: 5 Feb 2020 Last revised: 24 Sep 2021
Date Written: January 15, 2020
We develop a tractable equilibrium pricing model to explain observed characteristics in equity returns, VIX futures, S&P 500 options, and VIX options data based on affine jump- diffusive state dynamics and representative agents endowed with Duffie-Epstein recursive preferences. A specific model aimed at capturing VIX options prices and other asset market data is shown to successfully replicate the salient features of consumption, dividends, and asset market data, including the first two moments of VIX futures returns, the average implied volatilities in SPX and VIX options, and first and higher-order moments of VIX options returns. We document a time variation in the shape of VIX option implied volatility and a time-varying hedging relationship between VIX and SPX options which our model both captures.
Keywords: VIX, VIX options, Dynamic Equilibrium, Duffie-Epstein, Variance Risk Premium
JEL Classification: G00, G10, G12, G13
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