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.

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.

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.

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

scholarly journals Risk Management for Bonds with Embedded Options

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 790
Author(s):  
Antonio Díaz ◽  
Marta Tolentino
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Interest Rate Models ◽  
Management Measures ◽  
Interest Rate Risk Management ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Rate Change

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

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 The Rising Cost of Climate Change: Evidence from the Bond Market

2021 ◽  
pp. 1-45
Author(s):  
Michael D. Bauer ◽  
Glenn D. Rudebusch
Keyword(s):  
Climate Change ◽  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Mitigation Strategies ◽  
Social Cost Of Carbon ◽  
Carbon Mitigation ◽  
Interest Rate Models ◽  
Real Rate ◽  
The Social

Abstract Social discount rates (SDRs) are crucial for evaluating the costs of climate change. We show that the fundamental anchor for market-based SDRs is the equilibrium or steady-state real interest rate. Empirical interest rate models that allow for shifts in this equilibrium real rate find that it has declined notably since the 1990s, and this decline implies that the entire term structure of SDRs has shifted lower as well. Accounting for this new normal of persistently lower interest rates substantially boosts estimates of the social cost of carbon and supports a climate policy with stronger carbon mitigation strategies.

Bonds and Interest Rates

2019 ◽  
pp. 257-271
Author(s):  
Tomas Björk
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Rate Theory ◽  
Forward Rates ◽  
Depth Study ◽  
Basic Concepts ◽  
Floating Rate

In this chapter the reader is introduced to the basic concepts of interest rate theory. Starting with a market for zero coupon bonds we define the relevant interest rates such as the short rate, the spot rates, and the forward rates. There is an in-depth study of the relations between the dynamics of these rates, and we also discuss some more applied topics as fixed coupon bonds, floating rate bonds, yields, duration, and convexity.

Implications of Central banks’ negative policy rates on financial stability

2018 ◽  
Vol 10 (2) ◽  
pp. 310-320
Author(s):  
Benjamin S. Kay
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Financial Stability ◽  
Global Economy ◽  
Content Type ◽  
Interest Rate Policy ◽  
Trade Offs ◽  
Negative Interest Rates ◽  
Rate Policy ◽  
Negative Interest Rate Policy

Purpose While central bankers have widely discussed the trade-offs of negative interest rates on monetary policy, the consequences of negative rates on financial stability are less well understood. The purpose of this paper is to examine the likely and possible financial stability consequences of a negative rates policy with particular focus on banks, short-term funding markets, foreign exchange markets, asset managers, pension funds and insurers. Design/methodology/approach It draws from international experience with negative interest rates to identify financial stability threats posed to any economy by negative interest rates, and it also highlights where the US experience is likely to differ. Findings In time, financial market threats and other logistical issues of a negative interest rate policy can be managed or overcome. Even cumulatively, these threats are likely to be small as long as the rates remain only modestly negative. However, if the rates remain negative for long periods or they become more sharply negative, the rewards of avoiding negative rates increase. Originality/value Does the negative interest rate policy directly or through these challenges of implementation present a substantial obstacle to achieving financial stability objectives? As policy rates go negative in a greater share of the global economy, the financial stability consequences remain poorly understood and under discussed.

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