Bjarne Astrup Jensen

Term Structure Models with Parallel and Proportional Shifts

The paper investigates the possibility of an arbitrage‐free model for the term structure of interest rates where the yield curve only changes through a parallel shift. HJM type forward rate models driven by a multidimensional Wiener process and by a general marked point process are considered. Within this general framework it is shown that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. It is also shown that there exists no nontrivial flat term structure model. The same analysis is repeated for a similar case, in which the yield curve only changes through proportional shifts.

The First Difference Property of the Present Value Operator

The present value of a future cash flow together with derived risk measures like duration and convexity are some of the most fundamental concepts in financial economics. Technological advances have greatly enhanced methods for numerical calculations of such magnitudes. Consequently, analytical expressions have been pushed into the background to the extent that they are rarely, if ever, found in modern textbooks, despite their widespread use in both the classroom and in the real world. This holds, a fortiori, for the derivations leading to these expressions.Analytical solutions are instructive for both students and practitioners as they help understand the qualitative behavior and outcome of numerical calculations and the driving forces behind.This paper derives closed form solutions for the present value and the derived risk measures for a number of commonly used payment streams. The derivations in the paper only use elementary arithmetic operations and avoid cumbersome differentiation operations as well as complicated summation exercises.

Bond returns and financial index numbers: Results from an intertemporal arbitrage free model

The purpose of this paper is to shed light on some qualitative properties of binomial lattice models by analysing the entire distribution of future values arising from simple bond investment strategies. Our analysis is carried out by first determining the arbitrage free developments of the initial term structure. Secondly, we use these developments to analyse the entire distribution of future values arising from simple investment strategies. Additionally, we analyse whether index numbers such as the yield to maturity and the duration and the convexity are useful in order to characterize these distributions.

Pricing Contingent Claims: First- and Second-Order Effects from Stochastic Interest Rate Development

Applying an intertemporal and arbitrage-free binomial lattice model for the development of the term structure of interest rates, we derive the equations that determine prices of interest rate contingent claims.