scholarly journals First-Passage Time Model Driven by Lévy Process for Pricing CoCos

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoshan Su ◽  
Manying Bai
Keyword(s):  
Closed Form ◽  
Lévy Process ◽  
First Passage Time ◽  
Passage Time ◽  
Levy Process ◽  
Closed Form Expression ◽  
Lévy Measure ◽  
First Passage ◽  
Time Model ◽  
Time Problem

Contingent convertible bonds (CoCos) are typical form of contingent capital that converts into equity of issuing firm or writes down if a prespecified trigger occurs. This paper proposes a general Lévy framework for pricing CoCos. The Lévy framework indicates that the difficulty in giving closed-form expression for CoCos price is the possible introduction of the Lévy process whose first-passage time problem has not been solved. According to characteristics of new Lévy measure after the measure transform, three specific Lévy models driven by drifted Brownian motion, spectrally negative Lévy process, and double exponential jump diffusion process are proposed to give the solution keeping the form of the driving process unchanged under the measure transform. These three Lévy models provide closed-form expressions for CoCos price while the latter two possess them up to Laplace transform, whose pricing results are given by combining with numerical Fourier inversion and Laplace inversion. Numerical results show that negative jumps have large influence on CoCos pricing and the Black-Scholes model would overestimate CoCos price by simply compressing jumps information into volatility while the other two models would give more accurate CoCos price by taking jump risk into consideration.

scholarly journals On first-passage-time and transition densities for strongly symmetric diffusion processes

1997 ◽  
Vol 145 ◽  
pp. 143-161 ◽  
Author(s):  
A. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Process ◽  
Closed Form ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Time Dependent ◽  
Closed Form Expression ◽  
First Passage ◽  
One Dimensional ◽  
Transition Functions

One dimensional diffusion processes have been increasingly invoked to model a variety of biological, physical and engineering systems subject to random fluctuations (cf., for instance, Blake, I. F. and Lindsey, W. C. [2], Abrahams, J. [1], Giorno, V. et al [10] and references therein). However, usually the knowledge of the ‘free’ transition probability density function (pdf) is not sufficient; one is thus led to the more complicated task of determining transition functions in the presence of preassigned absorbing boundaries, or first-passage-time densities for time-dependent boundaries (see, for instance, Daniels, H. E. [6], [7], Giorno, V. et al. [10]). Such densities are known analytically only in some special instances so that numerical methods have to be implemented in general (cf., for instance, Buono-core, A. et al [3], [4], Giorno, V. et al [11]). The analytical approach becomes particularly effective when the diffusion process exhibits some special features, such as the symmetry of its transition pdf. For instance, in [10] special symmetry conditions on the transition pdf of one-dimensional time-homogeneous diffusion process with natural boundaries are investigated to derive closed form results concerning the transition pdf’s and the first-passage-time pdf for particular time-dependent boundaries. On the other hand, by using the method of images, in [6] Daniels has obtained a closed form expression for the transition pdf of the standard Wiener process in the presence of a particular time-dependent absorbing boundary. It is interesting to remark that such density cannot be obtained via the methods described in [10], even though the considered process exhibits the kind of symmetry discussed therein.

scholarly journals A note on first passage probabilities of a Lévy process reflected at a general barrier

2018 ◽  
Vol 37 (2) ◽  
pp. 456-469
Author(s):  
Zbigniew Palmowski ◽  
Przemysław Świątek
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Lévy Process ◽  
First Passage Time ◽  
Passage Time ◽  
Levy Process ◽  
First Passage ◽  
The Central Limit Theorem ◽  
First Passage Probability ◽  
Random Barrier

A NOTE ON FIRST PASSAGE PROBABILITIES OF A LÉVY PROCESS REFLECTED AT A GENERAL BARRIERIn this paper we analyze a Lévy process reflected at a general possibly random barrier. For this process we prove the Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics.

Closed-form solutions for the first-passage-time problem and neuronal modeling

2015 ◽  
Vol 64 (2) ◽  
pp. 421-439 ◽  
Author(s):  
Aniello Buonocore ◽  
Luigia Caputo ◽  
Giuseppe D’Onofrio ◽  
Enrica Pirozzi
Keyword(s):  
Closed Form ◽  
First Passage Time ◽  
Passage Time ◽  
Neuronal Modeling ◽  
First Passage ◽  
Closed Form Solutions ◽  
Time Problem ◽  
First Passage Time Problem

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

scholarly journals An approximation for the inverse first passage time problem

2011 ◽  
Vol 43 (01) ◽  
pp. 264-275 ◽  
Author(s):  
Jing-Sheng Song ◽  
Paul Zipkin
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem

We propose an approximation for the inverse first passage time problem. It is similar in spirit and method to the tangent approximation for the original first passage time problem. We provide evidence that the technique is quite accurate in many cases. We also identify some cases where the approximation performs poorly.

First‐Passage Time Problem

1970 ◽  
Vol 47 (1B) ◽  
pp. 393-394 ◽  
Author(s):  
Jann‐Nan Yang ◽  
Masanobu Shinozuka
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem

AN IMPROVED APPROACH TO EVALUATE DEFAULT PROBABILITIES AND DEFAULT CORRELATIONS WITH CONSISTENCY

2016 ◽  
Vol 19 (05) ◽  
pp. 1650036 ◽  
Author(s):  
WEIPING LI ◽  
TIM KREHBIEL
Keyword(s):  
Risk Management ◽  
Closed Form ◽  
First Passage Time ◽  
Passage Time ◽  
Default Probability ◽  
Default Correlation ◽  
First Passage ◽  
Management Implications ◽  
Asset Correlation ◽  
Closed Form Formula

We provide (i) a simplified analytic closed form formula for evaluating joint default probability, (ii) an improved method to resolve the inconsistency between the univariate process underlying firm-specific default probability and the correlated bivariate process of the first-passage-time default correlation model, (iii) illustration of risk management implications from misspecification of the default state space. Our closed form formula provides a natural extension of previous structural first-passage-time models and shows the sensitivities of default correlation numerically with respect to the underlying asset correlation, obligor credit quality and time horizon. We emphasize the disparate credit risk management implications of our result in contrast to commonly used risk measurement methods.

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