Occupation times of Lévy-driven Ornstein–Uhlenbeck processes with two-sided exponential jumps and applications

Zhou, Jiang; Wu, Lan; Bai, Yang

doi:10.1016/j.spl.2017.01.021

Cited by 10 publications

(5 citation statements)

References 17 publications

(11 reference statements)

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“…From Lemmas 2.1 and 2.2 in [27], where the authors examined the occupation times of Ornstein-Uhlenbeck process with two-sided exponential jumps, we have the following results:…”

Section: Ornstein-uhlenbeck Process With Exponential Jumpsmentioning

confidence: 91%

General drawdown of general tax model in a time-homogeneous Markov framework

Avram¹,

Li²,

Li³

2018

Preprint

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Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure) and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative Lévy processes -see Avram, Vu, Zhou(2017), Li, Vu, Zhou(2017. In this paper, we further examine general drawdown related quantities for taxed time-homogeneous Markov processes, using the pathwise connection between general drawdown and tax process.

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“…From Lemmas 2.1 and 2.2 in [27], where the authors examined the occupation times of Ornstein-Uhlenbeck process with two-sided exponential jumps, we have the following results:…”

Section: Ornstein-uhlenbeck Process With Exponential Jumpsmentioning

confidence: 91%

General drawdown of general tax model in a time-homogeneous Markov framework

Avram¹,

Li²,

Li³

2018

Preprint

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“…[40], [18], [54], [19]) or only European-type geometric step options under more advanced models (cf. [10], [13], [52], [53]). Additionally, although the inclusion of jumps naturally raises questions about their importance, no clear investigation of jump risk on the price and hedging parameters of geometric step options has been provided yet.…”

Section: 2mentioning

confidence: 99%

“…[18]) geometric step options have constantly gained attention in both the financial industry and the academic literature (cf. [10], [13], [54], [52], [53], [19]). As a whole class of financial contracts written on an underlying asset, these options have the particularity to cumulatively and proportionally loose or gain value when the underlying asset price stays below or above a predetermined threshold and consequently offer a continuum of alternatives between standard options and (standard) barrier options.…”

mentioning

confidence: 99%

“…1 Although semi-analytical pricing results for European-type geometric step options were already obtained by other authors under similar asset dynamics (cf. [10], [52], [53]), we note that these results employed double Laplace transform techniques while our method only relies on a one-dimensional Laplace(-Carson) transform. Additionally, the current geometric step option pricing literature seems to either study the Black & Scholes framework (cf.…”

mentioning

confidence: 99%

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Geometric step options and Lévy models: Duality, PIDEs, and semi-analytical pricing

Farkas¹,

Mathys²

2022

FMF

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<p style='text-indent:20px;'>The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and duality relations and derive various characterizations for both European-type and American-type geometric double barrier step options. In particular, we are able to obtain a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step contracts and its maturity-randomized equivalent as well as to characterize the diffusion and jump contributions to these early exercise premiums separately by means of partial integro-differential equations and ordinary integro-differential equations. As an application of our characterizations, we derive semi-analytical pricing results for (regular) European-type and American-type geometric down-and-out step call options under hyper-exponential jump-diffusion models. Lastly, we use the latter results to discuss the early exercise structure of geometric step options once jumps are added and to subsequently provide an analysis of the impact of jumps on the price and hedging parameters of (European-type and American-type) geometric step contracts.</p>

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“…In quantitative finance, path-dependent derivatives that depend on the time spent in prescribed price regions have been considered in Dassios (1995), Yor (1995), Linetsky (1999), Fusai (2000), Cai et al (2010), Li et al (2013), Wu and Zhou (2016) and Zhou et al (2017). For instance, the payoff of a particular 'step' European call option has been defined as e −ρτ [S T − K] + where ρ is a depreciation rate, T is the maturity, S T is the underlying price at time T, K is the strike price, H is a price threshold and τ = T 0 1 {S t ≤H} dt is the cumulated time where the underlying price is below H, that is, the occupation measure of the set {t : S t ≤ H}.…”

Section: Related Literaturementioning

confidence: 99%

Implied Markov transition matrices under structural price models

Defourny

Moazeni

2021

Quantitative Finance

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This paper proposes an approach to compute the implied transition matrices from observations of market data on financial derivatives, when the price of the underlying originates from a structural model and the payoffs are received over a period of time. The structural price model involves a price formation mechanism which computes the price based on a set of Markovian inputs and constrained optimization processes. The developed inference method relies on a linear description of the derivative values in terms of occupation measures of the payoff duration. We establish closed-form expressions between occupation measures and state transitions, which then enable us to characterize implied state transition probabilities consistent with the market data on the derivative values. We develop methods to solve the optimization problem with the resulting nonlinear occupation measure equation. Numerical illustrations of the approach are presented for financial derivatives on network capacities. By applying the method to an electric network, we investigate the relation between financial transmission correct contract values and a range of implied probabilities of congestion in the network.

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Occupation times of Lévy-driven Ornstein–Uhlenbeck processes with two-sided exponential jumps and applications

Cited by 10 publications

References 17 publications

General drawdown of general tax model in a time-homogeneous Markov framework

General drawdown of general tax model in a time-homogeneous Markov framework

Geometric step options and Lévy models: Duality, PIDEs, and semi-analytical pricing

Implied Markov transition matrices under structural price models

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