Distribution Of Interest Rates Research Articles

Overnight Borrowing, Interest Rates and Extreme Value Theory

We examine the dynamics of extreme values of overnight borrowing rates in an inter-bank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates before the crisis. The examination of tails (extreme values) provides answers to such issues as what are the extreme movements expected in financial markets; have we already seen the largest moves; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations.

Estimating the Implied Distribution of the Future Short Term Interest Rate Using the Longstaff-Schwartz Model

This paper proposes the use of the two-factor term-structure model of Longstaff and Schwartz (1992a, LS) to estimate the risk-neutral density (RND) of the future short-term interest rate. The resulting RND can be interpreted as the market's estimate of the density of the future short-term interest rate. As such, it provides a useful financial indicator of the perceived uncertainty of future developments in the short-term interest rate. The LS approach used in this paper provides an alternative to option-based estimation procedures, which may be useful in situations here options markets are not sufficiently developed to allow estimation of the implied distribution from observed option prices. A simulation-based comparison of these two approaches reveals that the differences in the results are relatively small in magnitude, at least for short forecast horizons. Furthermore, the LS model is quite successful in capturing the asymmetries of the true distribution. It is therefore concluded that the LS model can be useful for estimating the distribution of future interest rates, when the purpose is to provide a general measure of the market's perceived uncertainty, for example as an indictor for monetary policy purposes.

Did markets expect Italy to join EMU? Evidence from options markets

This note quantifies the movements in the distribution of future short-term market interest rates in reaction to the selection of countries that were to participate in stage three of Economic and Monetary Union as of 1 January 1999. We conclude that, before the various national central banks and the European Monetary Institute published their convergence reports, financial markets were already convinced that Italy would participate. They furthermore interpreted these reports, when published, as an indication that Italy would indeed participate. The official decision in May 1998 therefore came as no surprise.

Distributional Properties of Spot and Forward Interest Rates

This article provides analysis of the distributional properties of spot and forward interest rates without imposing any ad hoc assumptions on the behavior of interest rates. Using the kernel density estimation method, we estimate the distributions of spot and forward interest rates in levels and first differences. By comparing the two distributions, we show that examination of interest rates in levels can provide incremental information about the data generation process. In addition, we examine whether commonly used distributions, like the normal and lognormal distribution, can provide an adequate description of interest rate distribution. Finally we examine a more flexible mixture of two distributions as an alternative characterization of the distribution of interest rate changes.

Mathematics of Derivative Securities

Foreword R. C. Merton Part I. Introduction: 1. Editors' introduction 2. Stochastic calculus and Markov methods L. C. G. Rogers 3. The risk premium in trading equilibria which support Black-Scholes option pricing S. D. Hodges and M. J. P. Selby 4. On the numeraire portfolio P. Artzner Part II. Option Pricing and Hedging: 5. Convergence of Snell envelopes and critical prices in the American Put N. J. Cutland, P. E. Kopp, W. Willinger and M. C. Wyman 6. Some combination of Asian, Parisian and Barrier options M. Yor, M. Chesnay, H. Geman and M. Jeanblanc-Pique 7. Co-movement term structure and the valuation of crack energy spread options A. Mbanefo 8. Pricing and hedging with Smiles B. Dupire 9. Filtering derivative security valuations from market prices R. J. Elliott, C. H. Lahaie and D. B. Madan 10. Option pricing in the presence of extreme fluctuations J.-P. Bouchard, D. Sornette and M. Potters 11. Hedging long maturity commodity commitments with short-dated futures contracts M. J. Brennan and N. I. Crew 12. Nonlinear financial markets: hedging and portfolio optimization J. Cvitanic 13. Semimartingales and asset pricing under constraints M. Frittelli 14. Option pricing in incomplete markets M. H. A. Davis 15. Option pricing and hedging in discrete time with transaction costs F. Mercurio and T. C. F. Vorst Part III. Term Structure and Interest Rate Derivatives: 16. Bond and bond option pricing based on the current term structure P. H. Dybvig 17. Dynamic models for yield curve evolution B. Flesaker and L. P. Hughston 18. General interest rate models and the universality of HJM M. W. Baxter 19. Swap derivatives in a Gaussian HJM framework A. Brace and M. Musiela 20. Modelling bonds and derivatives with default risk D. Lando 21. Term structure modelling under alternative official regimes S. H. Babbs and N. J. Webber 22. Interest rate distributions, yield curve modelling and monetary policy L. El-Jahel, H. Lindberg and W. Perraudin Part IV. Numerical Methods: 23. Numerical option pricing using conditioned diffusions S. K. Gandhi and P. J. Hunt 24. Numerical valuation of cross-currency swaps and swaptions M. A. H. Dempster and J. P. Hutton 25. Numerical methods for stochastic control problems in finance H. J. Kushner 26. Simulation methods for option pricing J. P. Lehoczky 27. New methodologies for valuing derivatives S. H. Paskov.

Modeling the conditional distribution of interest rates as a regime-switching process

This paper develops a generalized regime-switching (GRS) model of the short-term interest rate. The model allows the short rate to exhibit both mean reversion and conditional heteroskedasticity and nests the popular generalized autoregressive conditional heteroskedasticity (GARCH) and square root process specifications. The conditional variance process accommodates volatility clustering and dependence on the level of the interest rate. A first-order Markov process with state-dependent transition probabilities governs the switching between regimes. The GRS model is compared with various existing models of the short rate in terms of (1) the statistical fit of short-term interest rate data and (2) out-of-sample forecasting performance.

A Method to Determine Optimal Stand Data Acquisition Policies

Abstract A method to determine optimal forest stand data acquisition policies is presented. The method is based on a proposal about how timber management planning could be performed, recognizing that stand data cannot be exactly known. It is suggested that decisions be made using probability distributions of values in the calculations instead of point estimates. Within this planning framework, using Bayesian theory, a posterior distribution can be calculated if an inventory is carried out. The probabilities for different posterior distributions can also be calculated. As different distributions may imply different optimal harvest actions, the expected inoptimality losses from erroneous harvest decisions will decrease after an inventory. However, if an inventory is to be an adequate decision, the inventory cost must not be higher than the expected decrease in losses. The numerical results showed that the profitability of inventories depends to a large extent on factors such as the interest rate, stumpage value, compartment size, stand age, and prior distribution of true stand volume. We found inventories to be most profitable if they were undertaken well ahead of calculated optimal harvests. Moreover, we also found that a series of moderately precise but cheap inventories was superior to one single very precise but expensive inventory. For. Sci. 40(4):630-649.

Asymptotic behavior and optimal properties of a consumption-investment model with variable time preference

This paper analyzes the convergence properties and the determination of an optimal consumption path in the consumption-investment model of Uzawa (1968). Sufficient conditions for the existence and uniqueness of the optimal path are presented. Components of the utility functional are recovered when the optimal path is piecewise affine. The model is applied to the determination of the interest rate and income distribution under time preference differentials.