This paper reviews and puts in context some of our recent work on stochastic volatility modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and stochastic volatility, (ii) OU based volatility models, (iii) exact option pricing, (iv) realised...

We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of...

We derive a closed-form expansion of option prices in terms of Black-Scholes prices and higher-order Greeks. We show how the true price of an option less its Black-Scholes price is given by a series of premiums on higher-order risks that are not priced under the Black-Scholes model assumptions....

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 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...