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

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.

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

Journal of Applied Probability ◽

10.1239/jap/1354716661 ◽

2012 ◽

Vol 49 (4) ◽

pp. 1119-1133 ◽

Cited By ~ 4

Author(s):

Lijun Bo ◽

Chen Hao

Keyword(s):

Laplace Transforms ◽

First Passage Times ◽

Square Root ◽

First Passage ◽

Brownian Motions ◽

Constant Elasticity ◽

Constant Elasticity Of Variance ◽

Geometric Brownian Motions ◽

Reflecting Barriers ◽

Passage Times

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First-passage times of two-dimensional Brownian motion

Advances in Applied Probability ◽

10.1017/apr.2016.64 ◽

2016 ◽

Vol 48 (4) ◽

pp. 1045-1060 ◽

Cited By ~ 7

Author(s):

Steven Kou ◽

Haowen Zhong

Keyword(s):

Brownian Motion ◽

Analytical Solutions ◽

Laplace Transforms ◽

First Passage Times ◽

Absolute Difference ◽

Two Dimensional ◽

First Passage ◽

Quantitative Finance ◽

The 1960S ◽

Passage Times

AbstractFirst-passage times (FPTs) of two-dimensional Brownian motion have many applications in quantitative finance. However, despite various attempts since the 1960s, there are few analytical solutions available. By solving a nonhomogeneous modified Helmholtz equation in an infinite wedge, we find analytical solutions for the Laplace transforms of FPTs; these Laplace transforms can be inverted numerically. The FPT problems lead to a class of bivariate exponential distributions which are absolute continuous but do not have the memoryless property. We also prove that the density of the absolute difference of FPTs tends to ∞ if and only if the correlation between the two Brownian motions is positive.

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Simulation of First-Passage Times for Alternating Brownian Motions

Methodology And Computing In Applied Probability ◽

10.1007/s11009-005-1481-3 ◽

2005 ◽

Vol 7 (2) ◽

pp. 161-181 ◽

Cited By ~ 8

Author(s):

A. Di Crescenzo ◽

E. Di Nardo ◽

L. M. Ricciardi

Keyword(s):

First Passage Times ◽

First Passage ◽

Brownian Motions ◽

Passage Times

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Extremes and First Passage Times of Correlated Fractional Brownian Motions

Stochastic Models ◽

10.1080/15326349.2014.903159 ◽

2014 ◽

Vol 30 (3) ◽

pp. 272-299 ◽

Cited By ~ 5

Author(s):

Enkelejd Hashorva ◽

Lanpeng Ji

Keyword(s):

First Passage Times ◽

First Passage ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Passage Times

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First passage times for subordinate Brownian motions

Stochastic Processes and their Applications ◽

10.1016/j.spa.2013.01.011 ◽

2013 ◽

Vol 123 (5) ◽

pp. 1820-1850 ◽

Cited By ~ 5

Author(s):

Mateusz Kwaśnicki ◽

Jacek Małecki ◽

Michał Ryznar

Keyword(s):

First Passage Times ◽

First Passage ◽

Brownian Motions ◽

Passage Times

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The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance

Abstract and Applied Analysis ◽

10.1155/2014/571724 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Chuancun Yin ◽

Yuzhen Wen ◽

Zhaojun Zong ◽

Ying Shen

Keyword(s):

Risk Model ◽

Diffusion Processes ◽

First Passage Time ◽

Laplace Transforms ◽

First Passage Times ◽

Jump Processes ◽

Closed Form Expression ◽

First Passage ◽

Time Problem ◽

Passage Times

This paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms, and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.

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