APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

Luca Capriotti (), Yupeng Jiang () and Gaukhar Shaimerdenova ()
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Luca Capriotti: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Yupeng Jiang: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Gaukhar Shaimerdenova: Department of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Al-Khawarizmi, Thuwal 23955-6900, Kingdom of Saudi Arabia

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 02, 1-16

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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024918500553

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