 A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementationMark Joshi and Riccardo Rebonato Quantitative Finance, 2003, vol. 3, issue 6, 458-469 Abstract: We present an extension of the LIBOR market model which allows for stochastic instantaneous volatilities of the forward rates in a displaced-diffusion setting. We show that virtually all the powerful and important approximations that apply in the deterministic setting can be successfully and naturally extended to the stochastic volatility case. In particular we show that (i) the caplet market can still be efficiently and accurately fit; (ii) that the drift approximations that allow the evolution of the forward rates over time steps as long as several years are still valid; (iii) that in the new setting the European swaption matrix implied by a given choice of volatility parameters can be efficiently approximated with a closed-form expression without having to carry out a Monte Carlo simulation for the forward rate process; and (iv) that it is still possible to calibrate the model virtually perfectly via simply matrix manipulations so that the prices of the co-terminal swaptions underlying a given Bermudan swaption will be exactly recovered, while retaining a desirable behaviour for the evolution of the term structure of volatilities. Date: 2003 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:3:y:2003:i:6:p:458-469 Ordering information: This journal article can be ordered from DOI: 10.1088/1469-7688/3/6/305 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
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