uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The perpetual American put option in jump-to-default models
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 89, no 2, p. 510-520Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2017. Vol. 89, no 2, p. 510-520
National Category
Probability Theory and Statistics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-313326DOI: 10.1080/17442508.2016.1267177ISI: 000392492800004OAI: oai:DiVA.org:uu-313326DiVA, id: diva2:1066800
Available from: 2017-01-19 Created: 2017-01-19 Last updated: 2017-11-29Bibliographically approved
In thesis
1. Valuation and Optimal Strategies in Markets Experiencing Shocks
Open this publication in new window or tab >>Valuation and Optimal Strategies in Markets Experiencing Shocks
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2017. p. 30
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 100
Keywords
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
National Category
Probability Theory and Statistics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-316578 (URN)978-91-506-2625-4 (ISBN)
Public defence
2017-05-03, room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2017-04-11 Created: 2017-03-14 Last updated: 2017-04-11

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full texthttp://www.tandfonline.com/doi/abs/10.1080/17442508.2016.1267177

Authority records BETA

Dyrssen, Hannah

Search in DiVA

By author/editor
Dyrssen, Hannah
By organisation
Applied Mathematics and StatisticsAnalysis and Probability Theory
In the same journal
Stochastics: An International Journal of Probablitiy and Stochastic Processes
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 546 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf