Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options
Need to know
- This work proposes a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models.
- The method combines a forward equation for barrier options with a novel two-state particle method to estimate the driving Markovian projection.
- A step-by-step procedure is provided for a Heston-type local-stochastic volatility model with local vol-of-vol, as well as two path-dependent volatility models.
- The numerical tests show that all three models are seen to calibrate well within the market no-touch bid-ask spread.
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.
Copyright Infopro Digital Limited. All rights reserved.
As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (point 2.4), printing is limited to a single copy.
If you would like to purchase additional rights please email info@risk.net
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5.
If you would like to purchase additional rights please email info@risk.net
