Equilibrium short-rate models vs no-arbitrage models: Literature review and computational examples

Fractional Term Structure Models: No-arbitrage and Consistency

In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs in the same spirit of Guasoni et al [14, 15]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. ...

Lévy term structure models: No-arbitrage and completeness

SUMMARY: We study the term structure models which are driven by a Lévy process, from the point of view of arbitrage and completeness. Exactly as for the Heath–Jarrow–Morton model, which fits into our class of models, we observe that the conditions on the coefficients for having no arbitrage opportunity are rather stringent. For the completeness problem, the results are quite surprising: namely ...

LECTURE 7 Interest Rate Models I: Short Rate Models

Continuous - Time Short Rate Models

These notes provide an overview of singleand multi-factor models of the short rate. We will begin with a generic single-factor model where the dynamics of rt under the physical measure, P , are given. Following the approach of Vasicek, we then derive the PDE that must be satisfied by derivative security prices. We then use the martingale approach to give an alternative (and familiar) expression...

Spatial Representation: Discrete vs. Continuous Computational Models

Topological notions and methods are used in various areas of the physical sciences and engineering, and therefore computer processing of topological data is important. Separate from this, but closely related, are computer science uses of topology: applications to programming language semantics and computing with exact real numbers are important examples. The seminar concentrated on an important...