A Family of Term‐structure Models for Long‐term Risk Management and Derivative Pricing

Cairns, Andrew J. G.

doi:10.1111/j.0960-1627.2004.00198.x

Cited by 28 publications

(15 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…They find that these models produce substantially different results and recommend using an interest rate model that best describes interest rate dynamics. Cairns (2004) also considers the consistency between the model dynamics and what is observed in the historical data as a highly desirable model feature.…”

Section: Literature Reviewmentioning

confidence: 99%

On the Effect of Interest Rates Dynamics on Vietnamese Companies

Bao¹,

Hong²

2015

IJEF

View full text Add to dashboard Cite

In this paper we set out a framework that will help Vietnamese companies to enhance their interest rate risk management practices. We start by analysing time series of Vietnamese Treasury bill rates. Using the maximum likelihood method we calibrate to these data seven models of interest rate dynamics: Vasicek (1977), Cox, Ingersoll and Ross (1985), Chan, Karolyi, Longstaff and Sanders (1992), Ahn and Gao (1999), Ait-Sahalia (1996), two factor version of Cox, Ingersoll and Ross (1985), and AR(1)-GARCH(1,1). Then using calibrated model parameters we calculate risk measures such as Value at Risk or Expected Shortfall and project the interest rates over three months. Finally we study the resulting risk measures as well as distributions of interest rates generated by each model and provide guidance regarding suitability of these models for risk management purposes.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

On the Effect of Interest Rates Dynamics on Vietnamese Companies

Bao¹,

Hong²

2015

IJEF

View full text Add to dashboard Cite

show abstract

“…By equation (72) together with Proposition 5, we see in particular that long zero-coupon rates can never fall. One should note, incidentally, that although there is a superficial resemblance between the zero-coupon rates with compounding frequency κ, defined by (69), and the tail-Pareto rates with index λ, defined by (13), these systems are distinct, and their asymptotic behaviour is different. In fact, if the compounding frequency in the zero-coupon system is made tenordependent by setting κ tT = λ/(T − t) for fixed λ, then one obtains the tail-Pareto system.…”

Section: Asymptotics Of Exponential Ratesmentioning

confidence: 99%

Social Discounting and the Long Rate of Interest

Brody

Hughston

2013

SSRN Journal

View full text Add to dashboard Cite

The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zerocoupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in the setting of modern interest rate theory, and show that if the long "simple" interest rate (or Libor rate) is finite, then this rate (unlike the zero-coupon rate) acts viably as a state variable, the value of which can fluctuate randomly in line with other economic indicators. New interest rate models are constructed, under this hypothesis and certain generalizations thereof, that illustrate explicitly the good asymptotic behaviour of the resulting discount bond systems. The conditions necessary for the existence of such "hyperbolic" and "generalized hyperbolic" long rates are those of so-called social discounting, which allow for long-term cash flows to be treated as broadly "just as important" as those of the short or medium term. As a consequence, we are able to provide a consistent arbitrage-free valuation framework for the costbenefit analysis and risk management of long-term social projects, such as those associated with sustainable energy, resource conservation, and climate change.

show abstract

“…Leippold and Wu (2000) introduce the idea of an exponential-quadratic mapping between pure-discount bond prices and the state-variable vector leading to the quadratic term-structure approach. Flesaker and Hughston (1996) and Cairns (2004) consider a rather more complex integral expression for the price of a pure-discount bond as a function of the state variables; this has been termed the positive-interest rate model. There are, of course, other no-arbitrage mappings, but they find application in the pricing of contingent claims and are not particularly relevant given the practical risk-management focus of this paper.…”

Section: Modelsmentioning

confidence: 99%