This paper studies the pricing of variance and volatility swaps in four financial models. More specifically, the authors derive analytical formulas for fair discrete variance strikes in the Black-Scholes, Heston stochastic volatility, Merton jump-diffusion and Bates and Scott stochastic volatility with jumps models.
The authors study the effect of discrete sampling and jumps on variance strikes with the latter depending on direction and magnitude of jumps. Furthermore, the paper demonstrates that the convexity correction formula to approximate fair volatility strikes does not provide suitable estimates in jump-diffusion models. Such volatility strikes are computed by numerical means.
Finally, the authors demonstrate that all the aforementioned models, fair discrete variance and volatility strikes converge in a linear manner to fair continuous variance and volatility strikes, respectively.
Reviewer’s remark: The paper is well-written and of interest to experts in both discrete sampling as well as volatility and variance swaps.