A TWO-REGIME, STOCHASTIC-VOLATILITY EXTENSION OF THE LIBOR MARKET MODEL

2004 ◽  
Vol 07 (05) ◽  
pp. 555-575 ◽  
Author(s):  
RICCARDO REBONATO ◽  
DHERMINDER KAINTH
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Market Model ◽  
The Real ◽  
Libor Market Model

We propose a two-regime stochastic volatility extension of the LIBOR market model that preserves the positive features of the recently introduced (Joshi and Rebonato 2001) stochastic-volatility LIBOR market model (ease of calibration to caplets and swaptions, efficient pricing of complex derivatives, etc.) and overcomes most of its shortcomings. We show the improvements by analyzing empirically and theoretically the real and the model-produced change sin swaption implied volatility.

A JOINT EMPIRICAL AND THEORETICAL INVESTIGATION OF THE MODES OF DEFORMATION OF SWAPTION MATRICES: IMPLICATIONS FOR MODEL CHOICE

2002 ◽  
Vol 05 (07) ◽  
pp. 667-694 ◽  
Author(s):  
RICCARDO REBONATO ◽  
MARK JOSHI
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Principal Component ◽  
Covariance Matrices ◽  
Market Model ◽  
Necessary Condition ◽  
Model Choice ◽  
Libor Market Model ◽  
Instantaneous Volatility ◽  
Eigenvectors And Eigenvalues

We present a joint empirical/theoretical analysis of the changes in the implied volatility swaption matrix for two currencies (USD and DEM/EUR). We recognize the existence of a small number of recognizable shape patterns, and comment about the speed of transition between them. By Principal/Component/Analyzing the associated correlation and covariance matrices we highlight a non/trivial interpretation for the leading eigenvectors. We also compare the empirically obtained eigenvectors and eigenvalues with the corresponding quantities produced by the stochastic/volatility LIBOR market model of Joshi and Rebonato[10]. This allows us to perform a measure-independent comparison that is of intrinsic interest, and that can also provide a general blueprint for analyzing the realism of and choosing among similarly-fitting stochastic models. We find that mean reversion of the instantaneous volatility is a necessary condition in order to obatin the market-observed shape of the first eigenvector associated with the covariance matrix.

CURRENCY DERIVATIVES UNDER A MINIMAL MARKET MODEL WITH RANDOM SCALING

2005 ◽  
Vol 08 (08) ◽  
pp. 1157-1177 ◽  
Author(s):  
DAVID HEATH ◽  
ECKHARD PLATEN
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
European Options ◽  
Bessel Processes ◽  
Exchange Rate Dynamics ◽  
Volatility Model ◽  
Minimal Market Model ◽  
Implied Volatility Surfaces

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

MODERN LIBOR MARKET MODELS: USING DIFFERENT CURVES FOR PROJECTING RATES AND FOR DISCOUNTING

2010 ◽  
Vol 13 (01) ◽  
pp. 113-137 ◽  
Author(s):  
FABIO MERCURIO
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Market Model ◽  
New Paradigm ◽  
Yield Curves ◽  
Market Models ◽  
Forward Rates ◽  
Libor Market Model ◽  
Market Practice ◽  
Joint Evolution

We introduce an extended LIBOR market model that is compatible with the current market practice of building different yield curves for different tenors and for discounting. The new paradigm is based on modeling the joint evolution of FRA rates and forward rates belonging to the discount curve. We will start by analyzing the basic lognormal case, then we will add stochastic volatility. The dynamics of FRA rates under different measures will be obtained and closed form formulas for caplets and swaptions derived in the lognormal and Heston (1993) cases.

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