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The perpetual American put option in jump-to-default models
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
2017 (engelsk)Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 89, nr 2, s. 510-520Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We study the perpetual American put option in a general jump-to-default model, deriving an explicit expression for the price of the option.

We find that in some cases the optimal stopping boundary vanishes and thus it is not optimal to exercise the option before default occurs. Precise conditions for when this situation arises are given.

Furthermore we present a necessary and sufficient condition for convexity of the option price, and also show that a nonincreasing intensity is sufficient, but not necessary, to have convexity.

From this we also get conditions for when option prices are monotone in the model parameters.

sted, utgiver, år, opplag, sider
2017. Vol. 89, nr 2, s. 510-520
HSV kategori
Forskningsprogram
Matematik med inriktning mot tillämpad matematik
Identifikatorer
URN: urn:nbn:se:uu:diva-313326DOI: 10.1080/17442508.2016.1267177ISI: 000392492800004OAI: oai:DiVA.org:uu-313326DiVA, id: diva2:1066800
Tilgjengelig fra: 2017-01-19 Laget: 2017-01-19 Sist oppdatert: 2017-11-29bibliografisk kontrollert
Inngår i avhandling
1. Valuation and Optimal Strategies in Markets Experiencing Shocks
Åpne denne publikasjonen i ny fane eller vindu >>Valuation and Optimal Strategies in Markets Experiencing Shocks
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on.

The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices.

The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique.

Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

sted, utgiver, år, opplag, sider
Uppsala: Department of Mathematics, 2017. s. 30
Serie
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 100
Emneord
American options, optimal stopping, game options, jump diffusion, jump to default, free-boundary problems, early exercise premium, integral equation, parabolic pde, convexity, sequential testing, fixed-point approach
HSV kategori
Forskningsprogram
Matematik med inriktning mot tillämpad matematik
Identifikatorer
urn:nbn:se:uu:diva-316578 (URN)978-91-506-2625-4 (ISBN)
Disputas
2017-05-03, room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2017-04-11 Laget: 2017-03-14 Sist oppdatert: 2017-04-11

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Forlagets fullteksthttp://www.tandfonline.com/doi/abs/10.1080/17442508.2016.1267177

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