The fractional volatility model: No-arbitrage, leverage and risk measures

TL;DR

This paper introduces a fractional noise-driven stochastic volatility model that aligns with market data, explores its no-arbitrage and leverage properties, and discusses associated risk measures.

Contribution

It presents a novel fractional volatility model with two versions based on the dependence of stochastic drivers, analyzing its no-arbitrage, leverage, and risk measures.

Findings

Model aligns with empirical market data

Two versions exhibit different leverage behaviors

Discusses risk measures within the fractional volatility framework

Abstract

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behavior. Here, the no-arbitrage and incompleteness properties of the model are studied. Some risk measures are also discussed in this framework.