Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-25T06:27:32.476Z Has data issue: false hasContentIssue false
  • English
  • Français

First Passage Times of Constant-Elasticity-of-Variance Processes with Two-Sided Reflecting Barriers

Part of: Markov processes Special processes

Published online by Cambridge University Press:  30 January 2018

Lijun Bo  and
Chen Hao
Lijun Bo*
Affiliation:
Xidian University
Chen Hao*
Affiliation:
Xidian University
*
∗ Postal address: Department of Mathematics, Xidian University, No. 2 South Taibai Road, Xi'an 710071, P. R. China.
∗ Postal address: Department of Mathematics, Xidian University, No. 2 South Taibai Road, Xi'an 710071, P. R. China.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we explore the first passage times of constant-elasticity-of-variance (CEV) processes with two-sided reflecting barriers. The explicit Laplace transforms of the first passage times are derived. Our results can include analytic formulae concerning Laplace transforms of first passage times of reflected Ornstein–Uhlenbeck processes, reflected geometric Brownian motions, and reflected square-root processes.

Keywords

First passage timeCEV processreflecting barrier

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1119 - 1133
Copyright
© Applied Probability Trust 

References

Atlan, M. and Leblanc, B. (2006). Time-changed Bessel processes and credit risk. Preprint.Google Scholar
Bo, L., Wang, Y. and Yang, X. (2011). First passage times of (reflected) Ornstein–Uhlenbeck processes over random Jump boundaries. J. Appl. Prob. 48, 723–732.CrossRefGoogle Scholar
Bo, L., Wang, Y. and Yang, X. (2011). Some integral functionals of reflected SDEs and their applications in finance. Quant. Finance 11, 343–348.CrossRefGoogle Scholar
Bo, L., Zhang, L. and Wang, Y. (2006). On the first passage times of reflected O-U processes with two-sided barriers. Queueing Systems 54, 313–316.CrossRefGoogle Scholar
Bouchard, B. (2008). Optimal reflection of diffusions and barrier options pricing under constraints. SIAM J. Control Optimization 47, 1785–1813.CrossRefGoogle Scholar
Cox, J. C. (1975). Notes on option pricing I: constant elasticity of variance diffusions. J. Portfolio Manag. 23, 15–17.CrossRefGoogle Scholar
Davydov, D. and Linestsky, V. (2001). Pricing and hedging path-dependent options under the CEV process. Manag. Sci. 47, 949–965.CrossRefGoogle Scholar
Göing-Jaeschke, A. and Yor, M. (2003). A survey and some generalizations of Bessel processes. Bernoulli 9, 313–349.CrossRefGoogle Scholar
Goldstein, R. and Keirstead, W. (1997). On the term structure of interest rates in the presence of reflecting and absorbing boundaries. Working paper.CrossRefGoogle Scholar
Harrison, M. (1986). Brownian Motion and Stochastic Flow Systems. John Wiley, New York.Google Scholar
Leung, K. S. and Kwok, Y. K. (2007). Distribution of occupation times for constant elasticity of variance diffusion and the pricing of α-quantile options. Quant. Finance 7, 87–94.CrossRefGoogle Scholar
Revuz, D. and Yor, M. (1991). Continuous Martingales and Brownian Motion. Springer, Berlin.CrossRefGoogle Scholar
Trutnau, G. (2011). Pathwise uniqueness of the squared Bessel and CIR process with skew reflection on a deterministic time dependent curve. Stoch. Process. Appl. 121, 1845–1863.CrossRefGoogle Scholar
Ward, A. R. and Glynn, P. W. (2003). Properties of the reflected Ornstein–Uhlenbeck process. Queueing Systems 44, 109–123.CrossRefGoogle Scholar