Approximation Methods for Inhomogeneous Geometric Brownian Motion

16 Pages Posted: 11 Oct 2018

See all articles by Luca Capriotti

Luca Capriotti

University College London; NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Yupeng Jiang

University College London

Gaukhar Shaimerdenova

King Abdullah University of Science and Technology - Department of Computer, Electrical and Mathematical Sciences & Engineering

Date Written: October 8, 2018

Abstract

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.

Keywords: Inhomogeneous Geometric Brownian Motion; Constant Elasticity of Variance; Arrow-Debreu Security, Derivative Pricing; Power Series Expansions

Suggested Citation

Capriotti, Luca and Jiang, Yupeng and Shaimerdenova, Gaukhar, Approximation Methods for Inhomogeneous Geometric Brownian Motion (October 8, 2018). International Journal of Theoretical and Applied Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3247379

Luca Capriotti (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

Yupeng Jiang

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Gaukhar Shaimerdenova

King Abdullah University of Science and Technology - Department of Computer, Electrical and Mathematical Sciences & Engineering ( email )

Al-Khawarizmi
Thuwal, 23955
Saudi Arabia

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