Optimal discrete hedging of American options using an integrated approach to options with complex embedded decisions

Gerer, Johannes; Dorfleitner, Gregor

doi:10.1007/s11147-017-9137-3

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…In this area, in which existing approaches fail, our framework proves most fruitful and can be used to generate new insights. Gerer and Dorfleitner (2016) apply our results to the problem of pricing and realistically hedging American options featuring a complex interplay between exercise and hedging decisions. Based on the results provided in this article, they provide the optimal solution to the full problem, which is -to our knowledge -the first of its kind.…”

Section: Resultsmentioning

confidence: 98%

Time consistent pricing of options with embedded decisions

Dorfleitner

Gerer

2019

Rev Deriv Res

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Many financial contracts are equipped with exercise rights or other features enabling the parties to actively shape the contract's payoff. These decisions pose a great challenge for the pricing and hedging of such contracts. Yet, the literature lacks a consistent way of dealing with these decisions, and instead only provides methods for specific contracts and not transferable to other models. In this paper we present a framework that allows us to separate the treatment of the decisions from the pricing problem and derive a general pricing principle for the price of an option with decisions by both parties. To accomplish this we present a general version of the duality between acceptance sets and pricing functions, and use it to translate the pricing problem into the language of acceptance. Expressing certain aspects of economic behavior in this language is sufficient to fully eliminate the decisions from the problem. Further, we demonstrate why time consistent pricing functions are crucial when dealing with options with embedded decisions and how the ad-hoc pricing functions used in many contributions can be derived if time consistency is added to our minimal set of assumptions.

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Section: Resultsmentioning

confidence: 98%

Time consistent pricing of options with embedded decisions

Dorfleitner

Gerer

2019

Rev Deriv Res

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“…Black and Cox (1976); Geske (1977), and Vidal Nunes (2011)), and contracts with complex embedded decisions (e.g. Gerer and Dorfleitner (2018), and Battauz et al (2020)). There is a vast literature on the close-to-maturity valuation of finite-maturity American options (e.g.…”

Section: Introductionmentioning

confidence: 99%

Optimal exercise of American put options near maturity: A new economic perspective

et al. 2021

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The critical price $$S^{*}\left( t\right) $$ S ∗ t of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that $$S^{*}\left( t\right) $$ S ∗ t coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals $$S^{*}\left( t\right) $$ S ∗ t ’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of $$S^{*}\left( t\right) $$ S ∗ t and rigorously show the correspondence of an American option problem to an easier European option problem at maturity .

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Optimal discrete hedging of American options using an integrated approach to options with complex embedded decisions

Cited by 2 publications

References 21 publications

Time consistent pricing of options with embedded decisions

Time consistent pricing of options with embedded decisions

Optimal exercise of American put options near maturity: A new economic perspective

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