Explosive behavior in the black–derman–toy model

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We consider the simulation of the Black–Derman–Toy (BDT) model with log-normally distributed rates in the spot measure, in discrete time and with a continuous state variable. We note an explosive behavior in the Eurodollar futures convexity adjustment at a critical value of the volatility, which depends on maturity, rate tenor, and simulation time step size. In the limit of a very small time step, this singularity appears for any volatility, and reproduces the Hogan–Weintraub singularity, which is generic for short-rate interest rate models with lognormally distributed rates. The singular behavior arises from a region in the state space which is usually truncated off in finite difference and tree methods, or is very poorly sampled in Monte Carlo methods, and thus is not observed under usual simulation methods.

Original languageEnglish
Title of host publicationInterdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
EditorsRoman N. Makarov, Roderick V. N. Melnik, Ilias S. Kotsireas, Hasan Shodiev, Monica G. Cojocaru, Monica G. Cojocaru, Roman N. Makarov, Roderick V. N. Melnik, Ilias S. Kotsireas, Hasan Shodiev
Pages361-366
Number of pages6
DOIs
StatePublished - 2015
EventInternational Conference on Applied Mathematics, Modelling and Computational Science, AMMCS 2013 - Waterloo, Canada
Duration: 26 Aug 201330 Aug 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume117
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Applied Mathematics, Modelling and Computational Science, AMMCS 2013
Country/TerritoryCanada
CityWaterloo
Period26/08/1330/08/13

Fingerprint

Dive into the research topics of 'Explosive behavior in the black–derman–toy model'. Together they form a unique fingerprint.

Cite this