A simple approximation for the no-arbitrage drifts in Libor market model–SABR-family interest-rate models

2015 ◽  
Vol 19 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Riccardo Rebonato
Keyword(s):  
Interest Rate ◽  
Market Model ◽  
Simple Approximation ◽  
Interest Rate Models ◽  
No Arbitrage ◽  
Libor Market Model

LIBOR market model with multiplicative basis

2018 ◽  
Vol 05 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Yangfan Zhong
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Slight Modification ◽  
Cash Flows ◽  
Market Model ◽  
Interest Rate Models ◽  
Forward Rates ◽  
Libor Market Model ◽  
Multiplicative Basis ◽  
Negative Interest Rates

The study on the multiple-curve interest rate models becomes increasingly active since the 2007 credit crunch, for which one curve, typically the OIS curve, is used for discounting purpose, while the LIBOR curves (associated with various market tenors) are used for projecting the future cash flows. In this work, we extend the standard LIBOR market model to accommodate such multiple-curve setting by means of a multiplicative basis. The multiplicative basis is modeled as an exponential function of multi-factor square-root processes. Under the multiplicative basis setup, the OIS forward rates are correlated with the implied (additive) LIBOR-OIS spreads. We then derive closed-form pricing formulas for caplet, swaption, and interest rate futures in the multiplicative basis framework. In particular, we show that the valuation of caplet and swaption can be easily computed by a proper integral of real-valued functions, which facilitates the calibration of our model. Finally, we discuss a slight modification of our model to allow for negative interest rates.

A Review of No Arbitrage Interest Rate Models

2012 ◽  
Author(s):  
Gerald W. Buetow ◽  
Frank J. Fabozzi ◽  
James Sochacki
Keyword(s):  
Interest Rate ◽  
Interest Rate Models ◽  
No Arbitrage

scholarly journals Valuation of Quanto Floating Range Notes under the Cross-Currency LIBOR Market Model

2015 ◽  
Vol 7 (12) ◽  
pp. 70 ◽  
Author(s):  
Chi-Hsun Chou ◽  
Tsung-Yu Hsieh ◽  
Son-Nan Chen
Keyword(s):  
Exchange Rate ◽  
Interest Rate ◽  
Market Model ◽  
Model Parameters ◽  
Rate Process ◽  
Multifactor Model ◽  
Libor Market Model ◽  
Empirical Results ◽  
The Cross ◽  
The Exchange Rate

<p>In this paper, we propose analytical valuation formulae for three types of quanto floating range notes based on the cross-currency LIBOR market model. The dynamics of forward LIBOR rates is a multifactor model that incorporates both the domestic and foreign interest rate process and the exchange rate process in a cross-currency environment. The derived formulae are analytically tractable and easy to implement in practice. The model parameters can be extracted directly from market quantities. We show that the empirical results are more accurate and robust than the results ofMonte Carlosimulation.</p>

BOND MARKET MODEL

2006 ◽  
Vol 09 (04) ◽  
pp. 577-596 ◽  
Author(s):  
ROBERTO BAVIERA
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Bond Market ◽  
Market Model ◽  
Structure Model ◽  
Over The Counter ◽  
Term Structure Model ◽  
Libor Market Model ◽  
Bond Options ◽  
Interest Rate Term Structure

We describe the Bond Market Model, a multi-factor interest rate term structure model, where it is possible to price with Black-like formulas the three classes of over-the-counter plain vanilla options. We derive the prices of caps/floors, bond options and swaptions. A comparison with Libor Market Model and Swap Market Model is discussed in detail, underlining advantages and limits of the different approaches.

AN EFFICIENT CALIBRATION METHOD FOR THE MULTI-FACTOR LIBOR MARKET MODEL AND ITS APPLICATION TO THE JAPANESE MARKET

2006 ◽  
Vol 09 (07) ◽  
pp. 1123-1139 ◽  
Author(s):  
HIDETOSHI TANIMURA ◽  
YUJI YAMADA
Keyword(s):  
Interest Rate ◽  
Empirical Analysis ◽  
Correlation Matrix ◽  
Computational Procedure ◽  
Calibration Method ◽  
Market Model ◽  
Japanese Market ◽  
Libor Market Model ◽  
The Empirical Analysis ◽  
Implied Correlation

In this paper an efficient calibration method for the multi-factor LIBOR Market Model (LMM) is proposed and is applied for the Japanese interest rate market. At first the joint calibration method in the cap and swaption market is demonstrated using a new parameterization for the correlation matrix in the LMM. Then we implement the proposed methodology for calibrating the Japanese cap and swaption markets, where the computational procedure is shown to be tractable and provides a practical estimation for the implied correlation matrix in the LMM. The empirical analysis also illustrates that Black's swaption volatilities through our calibration fit the market data almost exactly and that the estimated implied correlation matrix is smooth and stable.

scholarly journals AN EFFICIENT LATTICE ALGORITHM FOR THE LIBOR MARKET MODEL

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rate ◽  
Market Model ◽  
Approximation Methods ◽  
Libor Market Model ◽  
Forward Measure ◽  
Quick Turnaround ◽  
Fast Drift ◽  
Lattice Algorithm ◽  
Viable Method ◽  
Lattice Approach

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.

scholarly journals AN EFFICIENT LATTICE ALGORITHM FOR THE LIBOR MARKET MODEL

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rate ◽  
Market Model ◽  
Approximation Methods ◽  
Libor Market Model ◽  
Forward Measure ◽  
Quick Turnaround ◽  
Fast Drift ◽  
Lattice Algorithm ◽  
Viable Method ◽  
Lattice Approach

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.

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