Occupation times of hyper-exponential jump diffusion processes with application to price step options

Wu, Lan; Zhou, Jiang

doi:10.1016/j.cam.2015.09.001

Cited by 13 publications

(17 citation statements)

References 17 publications

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“…Closed-form formulas for European-style double barrier step options are obtained by Davydov & Linetsky (2002). European Step options are also studied under a class of nonlinear volatility diffusions by Campolieti, Makarov, & Wouterloot (2013) and hyper-exponential jump-diffusion processes by Wu & Zhou (2016). Xing & Yang (2013) consider American-style step options, for which the adjustment factor is based on the occupation time from the inception date to the exercise date.…”

Section: Introductionmentioning

confidence: 99%

American step options

Detemple

Abdou

Moraux³

2020

European Journal of Operational Research

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This paper examines the valuation of American knockout and knock-in step options. The structures of the immediate exercise regions of the various contracts are identified. Typical properties of American vanilla calls, such as uniqueness of the optimal exercise boundary, upconnectedness of the exercise region or convexity of its t-section, are shown to fail in some cases. Early exercise premium representations of step option prices, involving the Laplace transforms of the joint laws of Brownian motion and its occupation times, are derived. Systems of coupled integral equations for the components of the exercise boundary are deduced. Numerical implementations document the behavior of the price and the hedging policy. The paper is the first to prove that finite maturity exotic American Options written on a single underlying asset can have multiple disconnected exercise regions described by a triplet of coupled boundaries.

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Section: Introductionmentioning

confidence: 99%

American step options

Detemple

Abdou

Moraux³

2020

European Journal of Operational Research

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“…In fact, after some simple calculations, we obtain that formula (3.31) will reduce to the results given by Corollary 3.9 in [18].…”

Section: Examplesmentioning

confidence: 58%

“…where we have used the following result: 2 From the proof given in the Appendix A of Wu and Zhou [18], we obtain that V…”

Section: Proof Of Proposition 41mentioning

confidence: 99%

Occupation Times of General Lévy Processes

Zhou

2016

J Theor Probab

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For an arbitrary Lévy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results are important not only for the study of stochastic processes, but also for financial applications.

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“…In this section, assume that b ∈ R, s > 0, p > −s and −ϑ < 3 · q < η. The objection is to deduce the expression of The main results are given in Theorem 3.1, and for its derivation, we improve the approach in Wu and Zhou (2016). Especially, the technic used in proving V ′ (b−) = V ′ (b+) in Lemma 3.1 (will be presented after the proof of Theorem 3.1) is new and novel, and is expected to give some motivations to the investigation on the occupation times of Ornstein-Uhlenbeck processes driven by more general Lévy processes and other stochastic processes.…”

Section: Resultsmentioning

confidence: 99%