Approximation Methods for Inhomogeneous Geometric Brownian Motion

Luca Capriotti, Yupeng Jiang, Gaukhar Shaimerdenova

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We present an accurate and easy-to-compute approximation of the transition probabilities and the associated Arrow-Debreu (AD) prices for the inhomogeneous geometric Brownian motion (IGBM) model for interest rates, default intensities or volatilities. Through this procedure, dubbed exponent expansion, transition probabilities and AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results—for time horizons up to several years—even when truncated after the first few terms. For farther time horizons, the exponent expansion can be combined with a fast numerical convolution to obtain high-precision results.
Original languageEnglish (US)
Pages (from-to)1850055
JournalInternational Journal of Theoretical and Applied Finance
Issue number02
StatePublished - Oct 16 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The views expressed in this paper are those of the authors, and do not necessarily express those of Credit Suisse Group. We are grateful to Andrea Macrina and the anonymous referee for suggestions, and a careful reading of the manuscript and to Fabio Mercurio for many useful discussions.


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