Local Stochastic Volatility Models: Calibration and Pricing

57 Pages Posted: 11 Jun 2014 Last revised: 15 Jul 2014

Date Written: July 14, 2014


We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models.

We describe calibration procedures, with special attention given to usage and solution of corresponding forward Kolmogorov PDE/PIDE, and outline powerful algorithms for estimation of model parameters. Emphasis is placed on presenting practical details regarding the setup and the numerical solution of both forward and backward PDEs/PIDEs obtained from the LSV models. Consequently we discuss specifics (based on our experience and best practices from literature) regarding choice of boundary conditions, construction of nonuniform spatial grids and adaptive temporal grids, selection of efficient and appropriate finite difference schemes (with possible enhancements), etc. We also show how to practically integrate specific features of various types of financial instruments within calibration and pricing settings.

We consider all questions and topics identified as most relevant during the selection, calibration and pricing procedures associated with local stochastic volatility models, providing answers (to the best of our knowledge), and present references for deeper understanding and for additional perspectives. In a nutshell, it is our intention to present here an effective roadmap for a successful LSV journey.

Keywords: Local stochastic volatility models, calibration, pricing, estimation, PDE, PIDE, jumps, regime switching, optimization, finite difference

JEL Classification: C13, C61, C63, G12, G13

Suggested Citation

Homescu, Cristian, Local Stochastic Volatility Models: Calibration and Pricing (July 14, 2014). Available at SSRN: https://ssrn.com/abstract=2448098 or http://dx.doi.org/10.2139/ssrn.2448098

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics