Sandwiched Volterra Volatility model: Markovian approximations and hedging

TL;DR

This paper introduces a Markovian approximation for complex non-Markovian stochastic volatility models driven by Volterra noise, enabling explicit computation of hedging strategies with proven error bounds and numerical validation.

Contribution

It proposes a novel Markovian approximation for SVV-models driven by Volterra noise, facilitating explicit hedging strategy computation and error analysis.

Findings

Effective Markovian approximation of non-Markovian models

Explicit hedging strategies with error estimates

Numerical simulations validating theoretical results

Abstract

We consider stochastic volatility dynamics driven by a general H\"older continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the explicit computation of quadratic hedging strategies. While the theoretical hedge is well-known in terms of the non-anticipating derivative for all square integrable claims, the fact that these models are typically non-Markovian provides is a challenge in the direct computation of conditional expectations at the core of the explicit hedging strategy. To overcome this difficulty, we propose a Markovian approximation of the model which stems from an adequate approximation of the kernel in the Volterra noise. We study the approximation of the volatility, of the prices and of the optimal mean-square hedge. We provide the corresponding error estimates. The work is completed with numerical simulations.