and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is … between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large … options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five …

Analytic solutions are found for prices of variance and volatility swaps under a new time-dependent stochastic model …

Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the … volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We …, we provide relatively simple proofs of some fundamental results related to variance swaps and volatility swaps. …

surface and variance swap rates. Moreover, the two-factor model is able to reproduce the shapes of the implied volatility …The stochastic volatility model of Heston (Rev Financ Stud 6(2):327–343, <CitationRef CitationID="CR19 …">1993</CitationRef>) has found difficulty in describing some of the important features of implied volatility dynamics, leading to a quest …

In this paper, we will explain how to perfectly hedge under Heston's stochastic volatility model with jump …. The hedging instruments we use to build the hedge will be as usual the stock and the bond, but also the Variance Swap (VS …) and a Credit Default Swap (CDS). These instruments are very natural choices in this setting as the VS hedges against …

volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are … that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore …

volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short …-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a … term due to the volatility of the volatility. This decomposition procedure does not need the volatility process to be …

motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the … "volatility" and without a time change; here these results are extended to the case of stochastic volatility models when the … modulator is fractional Brownian motion or a time change of it. (Volatility in fractional Black–Scholes models does not carry …