Valuing tradeability in exponential Lévy models

Mathys, Ludovic

doi:10.3934/qfe.2020021

Cited by 5 publications

(4 citation statements)

References 33 publications

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“…Additionally, we note that this transform is well-defined. Indeed, this was already shown in a slightly different context for standard (European-and American-type) options in [43] and directly follows from these results, for ρ ≤ 0 and • ∈ {E, A}, by means of the inequality DSC • (T , x; K, , ρ ) ≤ DSC • (T , x; K, , (0, 0)) =: C • (T , x; K).…”

Section: European-type Contractssupporting

confidence: 69%

“…Nevertheless, the same arguments as in Section 2.5.1 (cf. [43]) directly show that the right-hand side in (2.67) is well-defined for ρ ≤ 0 and any ϑ > 0. Furthermore, OIDE characterizations of the maturity-randomized American-type contract DSC A (•) as well as of the respective early exercise premiums can be derived using strong Markovian arguments.…”

Section: European-type Contractsmentioning

confidence: 89%

“…X (•) denotes the Lévy exponent of (X t ) t≥0 under the measure Q (1) . In fact, showing that (X t ) t≥0 is a Lévy process is not hard and can be done as in [43] (cf. also [20]).…”

Section: Discussionmentioning

confidence: 99%

“…We emphasize that smooth-fit at the boundary b * can be proved using the same approach as the one outlined in[43]; See also[46],[35].…”

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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Section: European-type Contractssupporting

confidence: 69%

Section: European-type Contractsmentioning

confidence: 89%

“…X (•) denotes the Lévy exponent of (X t ) t≥0 under the measure Q (1) . In fact, showing that (X t ) t≥0 is a Lévy process is not hard and can be done as in [43] (cf. also [20]).…”

Section: Discussionmentioning

confidence: 99%

“…We emphasize that smooth-fit at the boundary b * can be proved using the same approach as the one outlined in[43]; See also[46],[35].…”

mentioning

confidence: 99%

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