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Information and Default Risk in Financial Valuation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Description
Abstract [en]

This thesis consists of an introduction and five articles in the field of financial mathematics. The main topics of the papers comprise credit risk modelling, optimal stopping theory, and Dynkin games. An underlying theme in all of the articles is valuation of various financial instruments. Namely, Paper I deals with valuation of a game version of a perpetual American option where the parties disagree about the distributional properties of the underlying process, Papers II and III investigate pricing of default-sensitive contingent claims, Paper IV treats CVA (credit value adjustment) modelling for a portfolio consisting of American options, and Paper V studies a problem motivated by model calibration in pricing of corporate bonds.

In each of the articles, we deal with an underlying stochastic process that is continuous in time and defined on some probability space. Namely, Papers I-IV treat stochastic processes with continuous paths, whereas Paper V assumes that the underlying process is a jump-diffusion with finite jump intensity.

The information level in Paper I is the filtration generated by the stock value. In articles III and IV, we consider investors whose information flow is designed as a progressive enlargement with default time of the filtration generated by the stock price, whereas in Paper II the information flow is an initial enlargement. Paper V assumes that the default is a hitting time of the firm's value and thus the underlying filtration is the one generated by the process modelling this value.

Moreover, in all of the papers the risk-free bonds are assumed for simplicity to have deterministic prices so that the focus is on the uncertainty coming from the stock price and default risk.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, Uppsala University , 2016. , 27 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 95
Keyword [en]
pricing, valuation, American options, Dynkin games, optimal stopping problem, optimal stopping games, credit risk, default risk, information, filtration, enlargement of filtrations
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-287364ISBN: 978-91-506-2551-6 (print)OAI: oai:DiVA.org:uu-287364DiVA: diva2:922643
Public defence
2016-06-13, Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 2, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2016-05-23 Created: 2016-04-24 Last updated: 2016-05-23
List of papers
1. Dynkin Games With Heterogeneous Beliefs
Open this publication in new window or tab >>Dynkin Games With Heterogeneous Beliefs
2017 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 54, no 1, 236-251 p.Article in journal (Refereed) Published
Abstract [en]

We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions, then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.

Keyword
Dynkin game, heterogeneous belief, multiple Nash equilibria, optimal stopping theory
National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-287358 (URN)10.1017/jpr.2016.97 (DOI)000399075200016 ()
Funder
Swedish Research Council
Available from: 2016-04-24 Created: 2016-04-24 Last updated: 2017-05-15Bibliographically approved
2. PRICING OF DEFAULT-SENSITIVE CONTINGENT CLAIMS FOR INFORMED INVESTORS
Open this publication in new window or tab >>PRICING OF DEFAULT-SENSITIVE CONTINGENT CLAIMS FOR INFORMED INVESTORS
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study the problem of pricing default-sensitive contingent claims for an informed investor who observes the stock price process as well as possesses additional information containing the knowledge of the default time from the very beginning. Under the assumption that the underlying default-free market is complete for a regular investor, i.e. an agent who observes only the stock price, and that the defaultable market is arbitrage-free for the informed investor, we show that any default-sensitive contingent claim has a unique price for the informed investor. Moreover, this price can be expressed in terms of prices of default-free contingent claims for the regular investor.

National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-287359 (URN)
Available from: 2016-04-24 Created: 2016-04-24 Last updated: 2016-04-24
3. PRICING OF DEFAULT-SENSITIVE CONTINGENT CLAIMS FOR REGULAR INVESTORS
Open this publication in new window or tab >>PRICING OF DEFAULT-SENSITIVE CONTINGENT CLAIMS FOR REGULAR INVESTORS
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider a defaultable market with a savings account, a risky asset S, and default-sensitive contingent claims which are claims with pay-offs that depend on a default time of the company issuing the stock S. The default time is modelled as a stopping time with respect to the filltration generated by the value of the firm, which is not directly observable by a regular investor, who observes only the stock and the default when it happens. However, the stock price and the value of the firm are correlated and thus observations of the stock price maybe used to infer the information about the default time. We study the pricing problem of a default-sensitive contingent claim for the regular investor and show that the defaultable market is incomplete from his or her perspective, and hence one must deal with the problem of choosing a martingale measure. We approach this task with the so-called f-divergence approach.

National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-287360 (URN)
Available from: 2016-04-24 Created: 2016-04-24 Last updated: 2016-04-24
4. AMERICAN OPTIONS AND COUNTERPARTY RISK
Open this publication in new window or tab >>AMERICAN OPTIONS AND COUNTERPARTY RISK
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study a problem of pricing a contract consisting of two American options between two defaultable counterparties. We embed the default risk directly in the expected pay-off so that optimal exercise strategies automatically compensate for the default risk. The problem reduces to a zero-sum optimal stopping game and we state and prove a verication theorem. Moreover, we solve explicitly an example where Player 1 sells a perpetual American call to Player 2 and Player 2 sells a perpetual American put to Player 1; and where one of the players has exponentially distributed default time.

National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-287361 (URN)
Available from: 2016-04-24 Created: 2016-04-24 Last updated: 2016-04-24
5. DEFAULT BARRIERS IN JUMP-DIFFUSION MODELS
Open this publication in new window or tab >>DEFAULT BARRIERS IN JUMP-DIFFUSION MODELS
(English)Manuscript (preprint) (Other academic)
National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-287362 (URN)
Available from: 2016-04-24 Created: 2016-04-24 Last updated: 2016-04-24

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