Abstract
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.
Highlights
A variance swap pays the difference between the realized variance of some underlying asset and the fixed variance swap rate
We find that the bivariate quadratic model produces better forecasts of variance swap rates than the univariate quadratic and polynomial models, as well as the martingale model
We introduce a novel class of quadratic term structure models for variance swaps
Summary
A variance swap pays the difference between the realized variance of some underlying asset and the fixed variance swap rate. We study univariate polynomial specifications of higher order Part of the reason could be that variance swap data became available only recently We contribute to this line of research by proposing a novel quadratic term structure model, assessing its empirical performance, and studying dynamic optimal portfolios in this setting. In addition to stock and bond, in an affine setting, Liu and Pan (2003) extend the investment opportunity set to options, and Egloff, Leippold, and Wu (2010) to variance swaps We study, both from theoretical and empirical perspectives, dynamic optimal portfolios including variance swaps and index option in our quadratic setting with stock index jumps. Technical derivations and proofs are collected in the online appendix.
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