Path Shadowing Monte-Carlo

TL;DR

The paper introduces Path Shadowing Monte-Carlo, a method for predicting future financial paths by averaging over generated paths that match observed history, improving volatility and option price predictions.

Contribution

It presents a novel Path Shadowing Monte-Carlo approach that enhances future path prediction accuracy using a multi-scale financial model.

Findings

State-of-the-art volatility predictions

Outperforms existing models in option smile estimation

Reproduces key statistical properties of financial data

Abstract

We introduce a Path Shadowing Monte-Carlo method, which provides prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or `shadows', the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called `Scattering Spectra'. This model promotes diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on volatility roughness. Our method yields state-of-the-art predictions for future realized volatility and allows one to determine conditional option smiles for the S\&P500 that outperform both the current version of the Path-Dependent Volatility model and the option market itself.