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Approximation Methods For Inhomogeneous Geometric Brownian Motion

Author

Listed:
  • 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)

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.

Suggested Citation

  • Luca Capriotti & Yupeng Jiang & Gaukhar Shaimerdenova, 2019. "Approximation Methods For Inhomogeneous Geometric Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-16, March.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:02:n:s0219024918500553
    DOI: 10.1142/S0219024918500553
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    References listed on IDEAS

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