Path decomposition of a reflected Lévy process on first passage over high levels

2021 ◽  
Author(s):  
Philip S. Griffin
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
First Passage ◽  
Path Decomposition

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.

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 LAN property for a simple Lévy process

2014 ◽  
Vol 352 (10) ◽  
pp. 859-864 ◽  
Author(s):  
Arturo Kohatsu-Higa ◽  
Eulalia Nualart ◽  
Ngoc Khue Tran
Keyword(s):  
Lévy Process ◽  
Levy Process

scholarly journals On the optimal dividend problem for a spectrally negative Lévy process

2007 ◽  
Vol 17 (1) ◽  
pp. 156-180 ◽  
Author(s):  
Florin Avram ◽  
Zbigniew Palmowski ◽  
Martijn R. Pistorius
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Spectrally Negative Lévy Process ◽  
Optimal Dividend

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

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