TY - JOUR
T1 - Approximation Methods for Inhomogeneous Geometric Brownian Motion
AU - Capriotti, Luca
AU - Jiang, Yupeng
AU - Shaimerdenova, Gaukhar
N1 - 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.
PY - 2018/10/16
Y1 - 2018/10/16
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/629401
UR - https://www.worldscientific.com/doi/abs/10.1142/S0219024918500553
UR - http://www.scopus.com/inward/record.url?scp=85056909304&partnerID=8YFLogxK
U2 - 10.1142/s0219024918500553
DO - 10.1142/s0219024918500553
M3 - Article
SN - 0219-0249
VL - 22
SP - 1850055
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 02
ER -