Reconstructing Volatility: Pricing of Index Options under Rough Volatility

TL;DR

This paper extends the pricing and hedging framework for index options to incorporate non-Markovian and rough volatility dynamics, addressing limitations of previous local volatility models.

Contribution

It introduces a novel approach for index option pricing under rough volatility, expanding the applicability of large deviations methods beyond local volatility assumptions.

Findings

Effective pricing under rough volatility models

Enhanced hedging strategies for non-Markovian dynamics

Validation through numerical experiments

Abstract

In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all components of the index. We here present an extension applicable to non-Markovian dynamics and in particular the case of rough volatility dynamics.