Equivalence of interest rate models and lattice gases

Details Equivalence of interest rate models and lattice gases Equivalence of interest rate models and lattice gases

2012-04-04

arxiv.org/abs/1204.0915v1

Economy

Quantitative Finance

Computational Finance

7 pages, 1 figure

Scientific paper

We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t) = a(t) exp(x(t)). These models include the Black, Derman, Toy and Black, Karasinski models in the terminal measure. We show that such interest rate models are equivalent with lattice gases with attractive two-body interaction V(t1,t2)= -Cov(x(t1),x(t2)). We consider in some detail the Black, Karasinski model with x(t) an Ornstein, Uhlenbeck process, and show that it is similar with a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions V(x,y) = -\alpha (e^{-\gamma |x - y|} - e^{-\gamma (x + y)}). An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black, Derman, Toy model in the terminal measure.

Affiliated with

Also associated with

No associations

Rating

Equivalence of interest rate models and lattice gases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivalence of interest rate models and lattice gases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivalence of interest rate models and lattice gases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31957