Quadratic Variance Swap Models
77 Pages Posted: 23 Mar 2013 Last revised: 20 Dec 2014
Date Written: December 18, 2014
We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly facilitating empirical analysis. Various goodness-of-fit tests show that quadratic models fit variance swaps on the S&P 500 remarkably well, and outperform affine models. We solve a dynamic optimal portfolio problem in variance swaps, index option, stock index and bond. An empirical analysis uncovers robust features of the optimal investment strategy.
Keywords: stochastic volatility, variance swap, quadratic term structure, quadratic jump-diffusion, dynamic optimal portfolio
JEL Classification: C51, G13
Suggested Citation: Suggested Citation