We consider a modelling setup where the VIX index dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed-form expansions and sharp...

In this work we derive new closed-form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel....

We propose a novel non-structural method for hedging European options, relying on two model-independent results: First, under suitable regularity conditions, an option price can be disentangled into a linear combination of risk-neutral moments. Second, there exists an explicit approximate...

We propose a non-structural method to retrieve the risk-neutral density (RND) impliedby options on the CBOE Volatility Index (VIX). The methodology is based on orthogonalpolynomial expansions around a kernel density and yields the RND of the underlyingasset without the need for a parametric...