USLV: Unspanned Stochastic Local Volatility Model release_rev_ecf3f1aa-ec1c-4af4-a743-27f2d39e7763

by Igor Halperin, Andrey Itkin

Released as a 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.
In text/plain format

Type  article
Stage   submitted
Date   2013-03-27
Version   v2
Language   en ?
arXiv  1301.4442v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)

This is a specific, static metadata record, not necessarily linked to any current entity in the catalog.

Catalog Record
Revision: ecf3f1aa-ec1c-4af4-a743-27f2d39e7763