Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options

Author: 

Bain, A
Mariapragassam, M
Reisinger, C

Publication Date: 

26 March 2021

Journal: 

Journal of Computational Finance

Last Updated: 

2021-09-28T17:24:59.287+01:00

Issue: 

4

Volume: 

24

DOI: 

10.21314/JCF.2020.400

page: 

115-161

abstract: 

In this paper, we consider a large class of continuous semi-martingale models and propose a generic framework for their simultaneous calibration to vanilla and no-touch options. The method builds on the forward partial integro-differential equation (PIDE) derived by B. Hambly, M. Mariapragassam and C. Reisinger in their 2016 paper, “A forward equation for barrier options under the Brunick & Shreve Markovian projection”; this allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. We also use a novel two-state particle method to estimate the Markovian projection of the variance onto the spot and the running maximum. We detail a step-by-step procedure for a Heston-type local-stochastic volatility model with local volatility-of-volatility, as well as two path-dependent volatility models where the local volatility component depends on the running maximum.

Symplectic id: 

1104213

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article