Markovian Projection for the Local Stochastic Volatility Libor Market Model

2015 ◽  
Author(s):  
Osamu Tsuchiya
Keyword(s):  
Stochastic Volatility ◽  
Market Model ◽  
Libor Market Model

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.

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.

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