Titolo: Sandwiched Volterra volatility models, power law and option pricing
Abstract:
We consider a financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the solution to be “sandwiched” between two arbitrary functions chosen in advance. Hence the name Sandwiched Volterra Volatility (SVV) model. Targeting option pricing, we discuss the structure of local martingale measures in this market and we develop an algorithm of pricing options with discontinuous payoffs. Our tools rely on the study of Malliavin calculus, indeed the Malliavin differentiability of the equations and prices is studied. With these, we can also study the power law property of the SVV model.