No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

Modeling the Term Structure of Interest Rates: Where Do We Stand?

Pricing and Hedging Interest Rate Options: Evidence from Cap-Floor Markets

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.

Derivatives are alternative financial instruments which extend traders opportunities to achieve some financial goals. They are risk management instruments that are related to a data in the future, and also they react to uncertain prices. Study on pricing futures can provide useful tools to understand the stochastic behavior of prices to manage the risk of price volatility. Thus, this study evaluates commodity futures contracts by considering Ross (1995) one-factor future pricing model as a function of spot price, Gibson and Schwartz (1990) two-factor futures pricing model as a function of spot price and convenience yield and finally Schwartz (1997) three-factor futures pricing model as a function of spot price, convenience yield and instantaneous interest rate by adding jump to stochastic behavior of commodity spot price. For this purpose, it is assumed that spot price follows Jump-diffusion stochastic process with exponential probability distribution of jump domain. Finally, commodity pricing future relations in three basic models are presented as a function of above factor(s) and jump parameters by using Duffy-Pan-Singleton approach. JEL Classification: G12, G13

A No-Arbitrage Analysis of Macroeconomic Determinants of Term Structures and the Exchange Rate

In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model

In this paper we empirically compare a wide range of different term structure models when it comes to the pricing and, in particular, hedging of caps and swaptions. We analyze the influence of the number of factors on the hedging and pricing results, and investigate which type of rate or derivative price data should be used to estimate the model parameters to obtain the best hedging and pricing results. We use on interest rates, and cap and swaption prices from 1995 to 1999. The empirical results on the hedging of caps and swaptions show that, if the number of hedge instruments is equal to the number of factors, the multi-factor models outperform one-factor models in hedging caps and swaptions. However, if one uses a large set of hedge instruments, one-factor models perform as well as multi-factor models. In terms of pricing, we find that models with two or three factors imply better out-of-sample predictions of cap and swaption prices than one-factor models. Also, estimation on the basis of current derivative prices leads to more accurate out-of-sample prediction of cap and swaption prices than estimation on the basis of interest rate data.

The aim of this paper is to express hedging of interest rate risk and its problems with consequences in using of hedge accounting under accounting standard IAS 39 by insurance company. This paper focuses especially on hedge accounting problem connected with long duration of negative market interest rates. At first, the paper focuses on market risks and in detail on explanation of the interest rate risk. Then paper focuses on hedge accounting under IAS 39 and its principles generally. Then paper focuses on the efficiency testing of the interest rate gap by cash flow hedging and its problem during long duration of negative market interest rates. Efficiency testing is showed on practical example of hedging interest rate gap of the insurance company in the period of negative interest rates. This paper focuses on assessment of hedging efficiency and abstract away from inefficiency calculation.

Dynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the m yield curve factors from the LIBOR and swap rates in the first step and the n options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.

Bond issuers frequently immunise/hedge their interest rate exposure by means of interest rate swaps (IRS). The receiving leg matches all bond cash flows, while the pay leg requires floating rate coupon payments of form LIBOR plus a spread. The goal of hedging against interest rate risk is only achieved in full if the present value of this spread is zero. Using market data it is shown that under a traditional IRS hedging strategy an investor could still experience significant cash flow losses given a 1 per cent shift in the underlying benchmark yield curve. Consideration is given to the instantaneous interest rate risk of a bond portfolio that allows for general changes in interest rates. Two contributions are made. The paper analyses the size of hedging imperfections arising from the widening of the floating rate spread in a traditional swap contract and subsequently proposes two new practical, effective and analytically tractable swap structures: Structure 1: an improved parallel hedge swap, hedges against parallel shifts of the yield curve; and Structure 2: an improved non-parallel hedge swap, hedges against any movement of the swap curve. Analytical representations of these swaps are provided such that spreadsheet implementations are easily attainable.

A dynamic Nelson-Siegel yield curve model with Markov switching

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

This paper contributes to the literature as the first work of its kind to examine the role and importance of Divisia monetary aggregates and concomitant User Cost Price indices as superior monetary policy forecasting tools in a negative interest rate environment. We compare the performance of Divisia monetary aggregates with traditional simple-sum aggregates in several theoretical models and in a Bayesian VAR to forecast the exchange rates between the euro, the dollar and yuan at various horizons using quarterly data. We evaluate their performance against that of a random walk using two criteria: Root Mean Square Error ratios and the Clark-West statistic. We find that, under a free-floating exchange regime, superior Divisia monetary aggregates outperform their simple sum counterparts and the benchmark random walk in a negative interest rate environment, consistently.