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On the Snell envelope approach to optimal switching and pricing Bermudan options
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two papers related to systems of Snell envelopes. The first paper uses a system of Snell envelopes to formulate the problem of two-modes optimal switching for the full balance sheet in finite horizon. This means that the switching problem is formulated in terms of trade-off strategies between expected profit and cost yields, which act as obstacles to each other. Existence of a minimal solution of this system is obtained by using an approximation scheme. Furthermore, the optimal switching strategies are fully characterized.

The second paper uses the Snell envelope to formulate the fair price of Bermudan options. To evaluate this formulation of the price, the optimal stopping strategy for such a contract must be estimated. This may be done recursively if some method of estimating conditional expectations is available. The paper focuses on nonparametric estimation of such expectations, by using regularization of a least-squares minimization, with a Tikhonov-type smoothing put on the partial diferential equation which characterizes the underlying price processes. This approach can hence be viewed as a combination of the Monte Carlo method and the PDE method for the estimation of conditional expectations. The estimation method turns out to be robust with regard tothe size of the smoothing parameter.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , viii p.
Series
Trita-MAT, ISSN 1401-2286 ; 11:01
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-42274ISBN: 978-91-7501-108-0 (print)OAI: oai:DiVA.org:kth-42274DiVA: diva2:446606
Presentation
2011-10-20, 3721, Lindstedtsvägen 25, KTH, Stockholm, 15:00 (English)
Opponent
Supervisors
Note
QC 20111013Available from: 2011-10-13 Created: 2011-10-06 Last updated: 2011-10-13Bibliographically approved
List of papers
1. A Full Balance Sheet Two-modes Optimal Switching problem
Open this publication in new window or tab >>A Full Balance Sheet Two-modes Optimal Switching problem
(English)In: Mathematical Methods of Operations Research, ISSN 1432-2994, E-ISSN 1432-5217Article in journal (Other academic) Submitted
Abstract [en]

We formulate and solve a finite horizon full balance sheet two-modes optimal switching problem related to trade-off strategies between expected profit and cost yields. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy.

Keyword
real options, backward SDEs, Snell envelope, stopping time, optimal switching, impulse control, balance sheet, merger and acquisition
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-42154 (URN)
Note
QS 2011 QS 20120326Available from: 2011-10-05 Created: 2011-10-05 Last updated: 2017-12-08Bibliographically approved
2. Pricing Bermudan options: A nonparametric estimation approach
Open this publication in new window or tab >>Pricing Bermudan options: A nonparametric estimation approach
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A nonparametric alternative to the Longstaff-Schwartz estimation of conditional expectations is suggested for pricing of Bermudan options. The method is based on regularization of a least-squares minimization, with a Tikhonov-type smoothing put on the partial differential equation which characterizes the underlying price processes. This approach can hence be viewed as a combination of the Monte Carlo method and the PDE method for the estimation of conditional expectations. The estimation method turns out to be robust with regard to the size of the smoothing parameter.

Keyword
Optimal stopping, regularization, nonparametric estimation, conditional expectations, Bermudan options, Snell envelope.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-42155 (URN)
Note

QS 2011105

Available from: 2011-10-05 Created: 2011-10-05 Last updated: 2013-04-16Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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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
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