An Accompaniment to a Course on Interest Rate Modeling: With Discussion of Black-76, Vasicek and HJM Models and a Gentle Introduction to the Multivariate LIBOR Market Model

2012 ◽  
Author(s):  
Vasily Nekrasov
Keyword(s):  
Interest Rate ◽  
Market Model ◽  
Libor Market Model ◽  
Hjm Models

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.

scholarly journals EXPLOSIVE BEHAVIOR IN A LOG-NORMAL INTEREST RATE MODEL

2013 ◽  
Vol 16 (04) ◽  
pp. 1350023 ◽  
Author(s):  
DAN PIRJOL
Keyword(s):  
Phase Transition ◽  
Interest Rate ◽  
Interest Rates ◽  
Functional Model ◽  
Market Model ◽  
Qualitative Behavior ◽  
Rate Model ◽  
Libor Market Model ◽  
Interest Rate Model ◽  
Log Normal

We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at low and high volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rates derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.

Pricing in-arrears caps and ratchet caps under LIBOR market model with multiplicative basis

2018 ◽  
Vol 05 (03) ◽  
pp. 1850023
Author(s):  
Yangfan Zhong ◽  
Yanhui Mi
Keyword(s):  
Interest Rate ◽  
Simulation Method ◽  
Analytical Approximation ◽  
Market Model ◽  
Transform Method ◽  
Interest Rate Derivatives ◽  
Forward Rates ◽  
Libor Market Model ◽  
Multiplicative Basis ◽  
Variable Function

In Zhong (2018), LIBOR market model with multiplicative basis, International Journal of Financial Engineering, 5(2), we proposed a LIBOR market model with multiplicative basis, namely, the LMM-MB model, to model the joint evolution of the LIBOR rates and the OIS forward rates. This model leads to tractable pricing formulas for the standard interest rate derivatives such as the (vanilla) caplet, swaption and futures. In this paper, we study the pricing of some non-standard interest rate derivatives under the LMM-MB model, specifically the in-arrears (IA) cap and the ratchet cap. Similar to the vanilla caplet, we show that the pricing of the IA caplet can be readily computed by a proper integral of real-valued functions. We then derive an analytical approximation for the ratchet cap. In the case of non-zero spread, the ratchet cap can be approximated by using a two-dimensional fast Fourier transform method. In the case of zero spread, the ratchet cap can be computed from a proper integral of a single variable function. Numerical results reveal a good match of our close-form formulas with the Monte Carlo simulation method.

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