American step options

Detemple, Jérôme; Abdou, Souleymane Laminou; Moraux, Franck

doi:10.1016/j.ejor.2019.09.009

Cited by 9 publications

(16 citation statements)

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“…A European‐type equivalent to the problem (5) was considered under a risk‐neutral utility by Linetsky (1999) under a geometric Brownian motion model, which he named a step option. The American version of this option under the same model and utility and a finite maturity time was recently considered by Detemple, Abdou, and Moraux (2019).…”

Section: Introductionmentioning

confidence: 99%

When to sell an asset amid anxiety about drawdowns

Rodosthenous

Zhang

2020

Mathematical Finance

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We consider risk‐averse investors with different levels of anxiety about asset price drawdowns. The latter is defined as the distance of the current price away from its best performance since inception. These drawdowns can increase either continuously or by jumps, and will contribute toward the investor's overall impatience when breaching the investor's private tolerance level. We investigate the unusual reactions of investors when aiming to sell an asset under such adverse market conditions. Mathematically, we study the optimal stopping of the utility of an asset sale with a random discounting that captures the investor's overall impatience. The random discounting is given by the cumulative amount of time spent by the drawdowns in an undesirable high region, fine‐tuned by the investor's personal tolerance and anxiety about drawdowns. We prove that in addition to the traditional take‐profit sales, the real‐life employed stop‐loss orders and trailing stops may become part of the optimal selling strategy, depending on different personal characteristics. This paper thus provides insights on the effect of anxiety and its distinction with traditional risk aversion on decision making.

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Section: Introductionmentioning

confidence: 99%

When to sell an asset amid anxiety about drawdowns

Rodosthenous

Zhang

2020

Mathematical Finance

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“…[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.…”

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confidence: 99%

“…As noted in [19], (geometric) step options are mainly traded as OTC-contracts and quantifying their importance purely based on trading activities is not an evident task. However, the importance of (geometric) step options is not restricted to their trading volumes and improving our understanding of these options may be beneficial for several reasons.…”

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confidence: 99%

“…However, the importance of (geometric) step options is not restricted to their trading volumes and improving our understanding of these options may be beneficial for several reasons. As an example, [19] emphasizes that geometric step options can serve as benchmark for the analysis and design of certain occupation-times derivatives as well as related structured products. Moreover, they can help modeling financial decision-making and shed light on economic phenomena where discounting is linked to the path of the underlying process.…”

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confidence: 99%

“…Such features are particularly useful when studying executive stock options as well as R&D projects (cf. [49], [19]).…”

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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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American options with acceleration clauses

Battauz,

Staffolani

2024

Decisions Econ Finan

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Acceleration clauses shorten the residual life of an option when an acceleration condition is met. Acceleration clauses are frequent in warrants, American call options on traded stocks. In warrants with the acceleration clause, if an index (e.g. the average underlying stock) triggers an acceleration threshold, the American call option can be exercised on a much shorter maturity (e.g. 30 days). The actual time-to-maturity of an American option with an acceleration condition is therefore stochastic. In order to evaluate these contracts we first reduce the generic American option with stochastic time-to-maturity to a compound American option with constant maturity, and provide estimates for their prices. Finally we propose an efficient algorithm to price American call options with the acceleration clause in a binomial setting.

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American step options

Cited by 9 publications

References 50 publications

When to sell an asset amid anxiety about drawdowns

When to sell an asset amid anxiety about drawdowns

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

American options with acceleration clauses

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