Download this Complimentary Numerix Quantitative Research Paper

In this article, we propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the linearity-generating unspanned volatility term structure model by Carr et al. (2011) by adding a local volatility layer to it.

We outline efficient numerical schemes for pricing derivatives in this framework for a particular four-factor specification (two "curve" factors plus two "volatility" factors). We show that the dynamics of such a system can be approximated by a Markov chain on a two-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by direct (Kroneker) products of values of pairs of curve and volatility factors, respectively. The resulting Markov chain dynamics on such partly "folded" state space enables fast pricing by the standard backward induction. Using a nonparametric specification of the Markov chain generator, one can accurately match arbitrary sets of vanilla option quotes with different strikes and maturities.

Furthermore, we consider an alternative formulation of the model in terms of an implied time change process. The latter is specified nonparametrically, again enabling accurate calibration to arbitrary sets of vanilla option quotes.

Authors: Igor Halperin and Andrey Itkin

Download Numerix Research Paper

Complete the form below to download this complimentary research paper.

Select Form: 

Form #5: Research

Keep me informed of future research from Numerix:

Sign me up to receive "Thinking Derivatively" monthly newsletter by Numerix:

* Required fields
quantitative research

STIRs and OIS Futures in the Hull-White Model

video blog

Numerix: Pushing Boundaries to Create Breakthrough Technology

video blog

What is Numerix Oneview?

newsletter issue - Nov 5, 2019

Thinking Derivatively - November 2019 Issue

newsletter issue - Oct 8, 2019

Thinking Derivatively - October 2019 Issue

newsletter issue - Sep 10, 2019

Thinking Derivatively - September 2019 Issue

newsletter issue - Aug 12, 2019

Thinking Derivatively - August 2019 Issue

video blog

Accelerate Your LIBOR Transition

newsletter issue - Jul 17, 2019

Thinking Derivatively - July 2019 Issue

press release - Jun 21, 2019

New Book “Modern SABR Analytics” Authored by Numerix Focuses on How to Enhance the SABR Model for...

on-demand webinar

On-Demand Resource | Dawn of Alternative Reference Rates: Curve Construction Fundamentals

white paper

White paper | LIBOR Will Not Transition Quietly: What You Need to Know Now