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Interest Rate Models (interest + rate_models)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	80%

Selected Abstracts

Forecasting and Finite Sample Performance of Short Rate Models: International Evidence,

INTERNATIONAL REVIEW OF FINANCE, Issue 3-4 2005
SIRIMON TREEPONGKARUNA
ABSTRACT This paper evaluates the forecasting and finite sample performance of short-term interest rate models in a number of countries. Specifically, we run a series of in-sample and out-of-sample tests for both the conditional mean and volatility of one-factor short rate models, and compare the results to the random walk model. Overall, we find that the out-of-sample forecasting performance of one-factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data. In addition, we perform a series of Monte Carlo analyses similar to Chapman and Pearson to document the finite sample performance of the short rate models when ,3 is not restricted to be equal to one. Our results indicate the potential dangers of over-parameterization and highlight the limitations of short-term interest rate models. [source]

The Term Structure of Simple Forward Rates with Jump Risk

MATHEMATICAL FINANCE, Issue 3 2003
Paul Glasserman
This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives. [source]

On the Existence of Finite-Dimensional Realizations for Nonlinear Forward Rate Models

MATHEMATICAL FINANCE, Issue 2 2001
Tomas Björk
We consider interest rate models of the Heath,Jarrow,Morton type, where the forward rates are driven by a multidimensional Wiener process, and where the volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Using ideas from differential geometry as well as from systems and control theory, we investigate when the forward rate process can be realized by a finite-dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite-dimensional realization. A number of concrete applications are given, and all previously known realization results (as far as existence is concerned) for Wiener driven models are included and extended. As a special case we give a general and easily applicable necessary and sufficient condition for when the induced short rate is a Markov process. In particular we give a short proof of a result by Jeffrey showing that the only forward rate models with short rate dependent volatility structures which generically possess a short rate realization are the affine ones. These models are thus the only generic short rate models from a forward rate point of view. [source]

Zero-coupon bond prices in the Vasicek and CIR models: Their computation as group-invariant solutions,

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2008
W. Sinkala
Abstract We compute prices of zero-coupon bonds in the Vasicek and Cox,Ingersoll,Ross interest rate models as group-invariant solutions. Firstly, we determine the symmetries of the valuation partial differential equation that are compatible with the terminal condition and then seek the desired solution among the invariant solutions arising from these symmetries. We also point to other possible studies on these models using the symmetries admitted by the valuation partial differential equations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Equity swaps in a LIBOR market model

THE JOURNAL OF FUTURES MARKETS, Issue 9 2007
Ting-Pin Wu
This study extends the BGM (A. Brace, D. Gatarek, & M. Musiela, 1997) interest rate model (the London Interbank Offered Rate [LIBOR] market model) by incorporating the stock price dynamics under the martingale measure. As compared with traditional interest rate models, the extended BGM model is both appropriate for pricing equity swaps and easy to calibrate. The general framework for pricing equity swaps is proposed and applied to the pricing of floating-for-equity swaps with either constant or variable notional principals. The calibration procedure and the practical implementation are also discussed. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:893,920, 2007 [source]