Parisian options with jumps: a maturity–excursion randomization approach

Chesney, Marc; Vasiljević, Nikola

doi:10.1080/14697688.2018.1444785

Cited by 12 publications

(22 citation statements)

References 57 publications

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“…Most notably, we are able to derive a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step options 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 (PIDEs) and ordinary integro-differential equations (OIDEs). Our results translate the formalism introduced in [22] to the setting of geometric double barrier step contracts and generalize at the same time the ideas introduced in [17], [36] and [16] to Lévy-driven markets. Next, as an application of these 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 processes.…”

supporting

confidence: 67%

“…One possible choice is the Gaver-Stehfest algorithm that has the advantage to allow for an inversion of the transform on the real line and that has been successfully used by several authors in the option pricing literature (cf. [32], [30], [51], [26], [36], [16], [37]). We will also rely on this algorithm, i.e.…”

Section: )mentioning

confidence: 99%

“…This has been already investigated by other authors in a similar context (cf. [51], [36], [16]) where this approach has proven to deliver a good pricing accuracy. We will follow the idea of this literature and will provide in Section 4 numerical results for geometric down-and-out step call options under hyper-exponential jump-diffusion markets based on this ansatz.…”

Section: European-type Contractsmentioning

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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supporting

confidence: 67%

Section: )mentioning

confidence: 99%

Section: European-type Contractsmentioning

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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“…One possible choice is the Gaver-Stehfest algorithm that has the particularity to allow for an inversion of the transform on the real line and that has been successfully used by several authors for option pricing (cf. Kou & Wang, 2003;Kimura, 2010;Hofer & Mayer, 2013;Leippold & Vasiljević, 2017;Chesney & Vasiljevic, 2018). We will also rely on this algorithm, that is, we set…”

Section: Maturity-randomization and Oidesmentioning

confidence: 99%

“…One possible choice is the Gaver‐Stehfest algorithm that has the particularity to allow for an inversion of the transform on the real line and that has been successfully used by several authors for option pricing (cf. Kou & Wang, 2003; Kimura, 2010; Hofer & Mayer, 2013; Leippold & Vasiljević, 2017; Chesney & Vasiljevic, 2018). We will also rely on this algorithm, that is, we set

g_{N} false(t false) : = \sum_{k = 1}^{2 N} ζ_{k, N} LC (g) (\frac{k \log false(2 false)}{t}), N \in N, t > 0,

where the coefficients are given by

ζ_{k, N} : = \frac{{false(- 1 false)}^{N + k}}{k} \sum_{j = ⌊ (k + 1) / 2 ⌋}^{\min {k, N}} \frac{j^{N + 1}}{N!} (\frac{0pt}{N}) (\frac{0pt}{2 j}) (\frac{0pt}{j}), N \in N, 1 \leq k \leq 2 N,

with

⌊ a ⌋ : = sup {z \in Z : z \leq a}

, and will recover the original function

g (\cdot)

by means of the following relation

\lim_{N \to \infty} g_{N} false(t false) = g false(t false) .

More details on the Gaver‐Stehfest algorithm as well as formal proofs of the convergence re...…”

Section: Intra‐horizon Risk and Models With Jumpsmentioning

confidence: 99%

Intra‐Horizon expected shortfall and risk structure in models with jumps

Farkas

Mathys

Vasiljević

2021

Mathematical Finance

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Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach

Zhuang

Tang

2023

Journal of Futures Markets

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In this study, we create a novel American double‐barrier Parisian call option contract that may be utilized as an executive option for listed companies to incentivize staff and replace the classic American option. We address the option pricing problem by developing state variables to identify the price state and using the least‐squares Monte Carlo approach. We present several Lévy processes to simulate the movement path of the underlying asset. We discover that geometric Brownian motion and normal inverse Gaussian (NIG) process have successful outcomes, and NIG process has greater calculation accuracy than variance gamma process. The barrier width and window length are positively connected with the price of an American Parisian option, whereas the strike price is negatively correlated with it. Increasing the number of discrete periods of the contract will enhance the pricing accuracy.

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Parisian options with jumps: a maturity–excursion randomization approach

Cited by 12 publications

References 57 publications

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

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

Intra‐Horizon expected shortfall and risk structure in models with jumps

Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach

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