Option pricing in Sandwiched Volterra Volatility model

TL;DR

This paper introduces a novel stochastic volatility model driven by H"older continuous Gaussian Volterra processes, allowing the volatility to be constrained between two predetermined functions, and develops an option pricing algorithm using Malliavin calculus.

Contribution

The paper presents a new sandwiched volatility model with flexible bounds and applies Malliavin calculus for option pricing with discontinuous payoffs.

Findings

Model ensures volatility stays within specified bounds.

Analyzes measure structure and integrability of the model.

Develops a Malliavin calculus-based option pricing algorithm.

Abstract

We introduce a new model of financial market with stochastic volatility driven by an arbitrary H\"older 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 H\"older continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities as well as study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs.