Libor

Abstract: Basic Definitions and No Arbitrage.- Definitions and Notation.- No-Arbitrage Pricing and Numeraire Change.- From Short Rate Models to HJM.- One-factor short-rate models.- Two-Factor Short-Rate Models.- The Heath-Jarrow-Morton (HJM) Framework.- Market Models.- The LIBOR and Swap Market Models (LFM and LSM).- Cases of Calibration of the LIBOR Market Model.- Monte Carlo Tests for LFM Analytical Approximations.- The Volatility Smile.- Including the Smile in the LFM.- Local-Volatility Models.- Stochastic-Volatility Models.- Uncertain-Parameter Models.- Examples of Market Payoffs.- Pricing Derivatives on a Single Interest-Rate Curve.- Pricing Derivatives on Two Interest-Rate Curves.- Inflation.- Pricing of Inflation-Indexed Derivatives.- Inflation-Indexed Swaps.- Inflation-Indexed Caplets/Floorlets.- Calibration to market data.- Introducing Stochastic Volatility.- Pricing Hybrids with an Inflation Component.- Credit.- and Pricing under Counterparty Risk.- Intensity Models.- CDS Options Market Models.

Abstract: This article develops a multi-factor econometric model of the term structure of interest-rate swap yields. The model accommodates the possibility of counterparty default, and any differences in the liquidities of the Treasury and Swap markets. By parameterizing a model of swap rates directly, we are able to compute model-based estimates of the defaultable zero-coupon bond rates implicit in the swap market without having to specify a priori the dependence of these rates on default hazard or recovery rates. The time series analysis of spreads between zero-coupon swap and treasury yields reveals that both credit and liquidity factors were important sources of variation in swap spreads over the past decade. ALTHOUGH PLAIN VANILLA FIXED-for-floating interest-rate swaps comprise a major segment of the fixed-income derivative market, notably few econometric models for pricing swaps have been developed in the literature. Perhaps the primary reasons for this are: (i) swap contracts embody default risk and hence equilibrium or arbitrage-free term structure models developed for default-free government bond markets are not directly applicable to the swap market; (ii) empirical modeling of the default event underlying credit spreads on defaultable bonds and swaps has met with limited success at explaining the timeseries properties of spreads; and (iii) swap spreads are likely to depend on other factors such as liquidity that are not directly related to default events. Also, until recently, data have not been widely available. In this article we develop a multifactor econometric model of the term structure of U.S. fixedfor-floating interest-rate swap yields that accommodates many of the institutional features of swap markets. Specifically, using results in Duffie and Singleton (1996), we show that the fixed payment rate of a swap, assuming that the floating rate is London Interbank Offering Rate (LIBOR), can be expressed in terms of present values of net cash flows of the swap contract

Abstract: At the center of the financial market crisis of 2007-2008 was a highly unusual jump in spreads between the overnight inter-bank lending rate and term London inter-bank offer rates (Libor). Because many private loans are linked to Libor rates, the sharp increase in these spreads raised the cost of borrowing and interfered with monetary policy. The widening spreads became a major focus of the Federal Reserve, which took several actions -- including the introduction of a new term auction facility (TAF) --- to reduce them. This paper documents these developments and, using a no-arbitrage model of the term structure, tests various explanations, including increased risk and greater liquidity demands, while controlling for expectations of future interest rates. We show that increased counterparty risk between banks contributed to the rise in spreads and find no empirical evidence that the TAF has reduced spreads. The results have implications for monetary policy and financial economics.

Abstract: Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Ito calculus, basic probability theory, and real and complex analysis.