scholarly journals Extension of SABR Libor Market Model to handle negative interest rates

2020 ◽  
Vol 4 (1) ◽  
pp. 148-171
Author(s):  
Jie Xiong ◽  
◽  
Geng Deng ◽  
Xindong Wang
Keyword(s):  
Interest Rates ◽  
Market Model ◽  
Libor Market Model ◽  
Negative Interest Rates

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 numerical method to price European derivatives based on the one factor LIBOR Market Model of interest rates

2008 ◽  
Vol 2 (2) ◽  
pp. 568-589 ◽  
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Francesco Zirilli
Keyword(s):  
Interest Rates ◽  
Numerical Method ◽  
Market Model ◽  
Libor Market Model ◽  
The One

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.

MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR A PARTIAL DIFFERENTIAL EQUATIONS MODEL GOVERNING A RATCHET CAP PRICING IN THE LIBOR MARKET MODEL

2011 ◽  
Vol 21 (07) ◽  
pp. 1479-1498 ◽  
Author(s):  
A. PASCUCCI ◽  
M. SUÁREZ-TABOADA ◽  
C. VÁZQUEZ
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Interest Rates ◽  
Time Discretization ◽  
Fundamental Solutions ◽  
Market Model ◽  
Computational Time ◽  
Cauchy Problems ◽  
Partial Differential ◽  
Libor Market Model

In this paper, we present a mathematical model for pricing a particular financial product: the ratchet cap. This derivative product depends on certain interest rates (whose dynamics we assume that follow the LIBOR market model). The pricing model is rigorously posed in terms of a sequence of nested Cauchy problems associated to uniformly parabolic partial differential equations. First, for each problem the existence and uniqueness of solution is obtained. Next, this analysis allows to propose a new and more efficient numerical method based on the approximation by computable fundamental solutions of constant coefficient operators. The advantage in terms of computational time of this new modeling and analytically based approach is illustrated by comparison with the classically used Monte Carlo simulation and a characteristics Crank–Nicolson time discretization combined with finite elements strategy.

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