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Recovering a piecewise constant volatility from perpetual put option prices
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, 680-692 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we present a method to recover a time-homogeneous piecewise constant volatility from a finite set of perpetual put option prices. The whole calculation process of the volatility is decomposed into easy computations in many fixed disjoint intervals. In each interval, the volatility is obtained by solving a system of nonlinear equations.

Place, publisher, year, edition, pages
2010. Vol. 47, no 3, 680-692 p.
Keyword [en]
Perpetual put option, calibration of models, piecewise constant volatility
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-134147DOI: 10.1239/jap/1285335403ISI: 000282856000005OAI: oai:DiVA.org:uu-134147DiVA: diva2:372123
Available from: 2010-11-24 Created: 2010-11-22 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Optimal stopping and incomplete information in finance
Open this publication in new window or tab >>Optimal stopping and incomplete information in finance
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2011. 45 p.
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2011:24
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-164340 (URN)
Presentation
2012-01-17, 13:15 (English)
Supervisors
Available from: 2011-12-22 Created: 2011-12-19 Last updated: 2011-12-22Bibliographically approved
2. Calibration, Optimality and Financial Mathematics
Open this publication in new window or tab >>Calibration, Optimality and Financial Mathematics
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility.

In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices.

In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary.

In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary.

Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level.

Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2013. 25 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 83
Keyword
perpetual put option, calibration of models, piecewise constant volatility, optimal liquidation of an asset, incomplete information, optimal stopping, jump-diffusion model, optimal distribution of dividends, singular stochastic control, implied volatility, exponential Lévy models, short-time asymptotic behavior.
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-209235 (URN)978-91-506-2377-2 (ISBN)
Public defence
2013-11-29, Ångström, rum 2001, Ångströmslaboratoriet , Lägerhyddsvägen 1, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2013-11-07 Created: 2013-10-15 Last updated: 2013-11-07

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