Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options

TL;DR

This paper introduces a flexible calibration framework for local-stochastic and path-dependent volatility models, enabling efficient pricing of vanilla and no-touch options, with promising numerical results on EURUSD data.

Contribution

It develops a novel calibration method using forward PIDE and a two-states particle approach for complex volatility models, including local-stochastic and path-dependent types.

Findings

Models calibrate well within market bid-ask spreads.

The framework efficiently handles a wide range of strikes, barriers, and maturities.

Numerical tests show good fit to EURUSD market data.

Abstract

We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle method to estimate the Markovian projection of the variance onto the spot and running maximum. We detail a step-by-step procedure for a Heston-type local-stochastic volatility model with local vol-of-vol, as well as two path-dependent volatility models where the local volatility component depends on the running maximum. In numerical tests, we benchmark these new models against standard models for a set of EURUSD market data, all three models are seen to calibrate well within the market no-touch bid--ask.