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...

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant generating function, which can be obtained as solution of a...

We study the rank of the instantaneous or spot covariance matrix Σ(t) of a multidimensional continuous semi-martingale X(t). Given highfrequency observations X(i=n), i = 0; : : : ;n, we test the null hypothesis rank (Σ(t)) ≤ r for all t against local alternatives where the average (r + 1)st...

We explore whether the market variance risk premium (VRP) can be predicted. First, we propose a novel approach to measure VRP which distinguishes the investment horizon from the variance swap's maturity. We extract VRP from actual rather than synthetic S&P 500 variance swap quotes, thus avoiding...

We explore whether the market variance risk premium (VRP) can be predicted. First, we propose a novel approach to measure VRP which distinguishes the investment horizon from the variance swap's maturity. We extract VRP from actual rather than synthetic S&P 500 variance swap quotes, thus avoiding...

We consider a square-integrable semimartingale with conditionally independent increments and symmetric jump measure, and show that its discrete realized variance dominates its quadratic variation in increasing convex order. The result has immediate applications to the pricing of options on...

We consider the saddlepoint approximation methods for pricing derivatives whose payoffs depend on the discrete realized variance of the underlying price process of a risky asset. Most of the earlier pricing models of variance products and volatility derivatives use the quadratic variation...

This paper develops a new approach for variance trading. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the exact timing for rebalancing in the underlying. The...

We analyze the variance risk of commodity markets. We construct synthetic variance swaps and find significantly negative realized and expected variance swap payoffs in most markets. We find evidence of commonalities among the realized payoffs of commodity variance swaps. We also document...