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Wahlpflichtbereiches
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Titel
des Moduls
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Bewertung der Amerikanischen Optionen in Stochastischen Modellen der Finanzmärkten |
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in englischer Sprache
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A
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X
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Vorlesung |
Übung |
Umfang |
2 |
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Inhalt
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The pricing of derivative securities is one
of the interesting and important problems in the mathematical theory of
modern finance. A major part of the derivatives being traded at
financial markets are options
of the so-called American type,
which can be exercised by the
holders at any time up to maturity.
The natural mathematical problems arising by stochastic market modeling and
related to this type of contracts are to seek for optimal stopping times, at which the holder should exercise the
given contingent claims. The rational prices of such contracts are
given by the values of the corresponding optimal
stopping problems considered under some risk-neutral measures for the
underlying risky asset price processes in the efficient market models. It is
shown that the optimal stopping times in these problems are the first times
when the underlying price processes come into the regions restricted by the exercise boundaries. The explicit
expressions for the value functions and the boundaries are derived by means
of reducing the initial optimal stopping problems to the equivalent free-boundary
problems and then verifying the candidate solutions by using martingale
methods. In the lecture, the problems of pricing of standard and several
exotic American and more general game
contingent claims in different stochastic models of financial markets
will be considered. |
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Voraussetzungen
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Stochastik
I, II |
Regelsemester
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ab 6 Fachsemester |
Abschluss |
Prüfung |
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Prüfungszulassungsvor-aussetzung
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Prüfung |
Studienpunkte |
4 |
R = Reine Mathematik
A = Angewandte Mathematik