Bond market models with Lévy processes

Date

Dec 20, 2012

Time

2:00 PM - 3:00 PM

Speaker

Dr. Michal Barski

Affiliation

Universität Leipzig

Series

TUD Mathematik AG Analysis & Stochastik

Language

de

Main Topic

Mathematik

Other Topics

Mathematik

Host

Dr. Felix Lindner

Description

The talk will be devoted to the arbitrage-free modelling of the family of bond prices which satisfy some natural monotonicity properties. Let P(t; T; x) be a price at time t of a bond with maturity T and risk parameter x. The prices should be decreasing in T and increasing in x, but mathematical models do not preserve this monotonicity property even if they satisfy the severe no-arbitrage conditions. We will present conditions which imply no-arbitrage and monotonicity of the bond proces via examining properties of the corresponding Heath-Jarrow-Morton-Musiela equation. We will use the so called comparison results for a general SPDE presented in [3]. References [1] Barski, M., Zabczyk, J. : "Heath-Jarrow-Morton-Musiela equation with Levy perturbation", (2012), Journal of Dierential Equations, 253, 9, p. 2657-2697; [2] Barski M. : "Monotonicity of the CDO term strcture models", (2012), submitted; [3] Milian, A. : "Comparison theorems for stochastic evolution equation",(2002), Stochastics and Stochastics Reports, 72, 79-108.

Links

• AG Analysis & Stochastik

Last modified: Dec 12, 2012, 4:06:39 PM