Bonds with volatilities proportional to forward rates
Computational Finance
2009-11-06 v1 Probability
Pricing of Securities
Abstract
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields are formulated. It is shown that if the first derivative of the Levy-Khinchin exponent grows slower then logarithmic function then the answer is positive and if it is bounded from below by a fractional power function of any positive order then the answer is negative. Numerous examples including models with Levy measures of stable type are presented.
Keywords
Cite
@article{arxiv.0911.1119,
title = {Bonds with volatilities proportional to forward rates},
author = {Michal Baran and Jerzy Zabczyk},
journal= {arXiv preprint arXiv:0911.1119},
year = {2009}
}