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Properties of American option prices
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2004 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, Vol. 114, no 2, 265-278 p.Article in journal (Refereed) Published
Abstract [en]

We investigate some properties of American option prices in the setting of time- and level-dependent volatility. The properties under consideration are convexity in the underlying stock price, monotonicity and continuity in the volatility and time decay. Some properties are direct consequences of the corresponding properties of European option prices that are already known, and some follow by writing solutions of different stochastic differential equations as time changes of the same Brownian motion.

Place, publisher, year, edition, pages
2004. Vol. 114, no 2, 265-278 p.
National Category
Natural Sciences
URN: urn:nbn:se:uu:diva-92190DOI: 10.1016/j.spa.2004.05.002OAI: oai:DiVA.org:uu-92190DiVA: diva2:165175
Available from: 2004-10-08 Created: 2004-10-08 Last updated: 2016-05-02Bibliographically approved
In thesis
1. Selected Problems in Financial Mathematics
Open this publication in new window or tab >>Selected Problems in Financial Mathematics
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis, consisting of six papers and a summary, studies the area of continuous time financial mathematics. A unifying theme for many of the problems studied is the implications of possible mis-specifications of models. Intimately connected with this question is, perhaps surprisingly, convexity properties of option prices. We also study qualitative behavior of different optimal stopping boundaries appearing in option pricing.

In Paper I a new condition on the contract function of an American option is provided under which the option price increases monotonically in the volatility. It is also shown that American option prices are continuous in the volatility.

In Paper II an explicit pricing formula for the perpetual American put option in the Constant Elasticity of Variance model is derived. Moreover, different properties of this price are studied.

Paper III deals with the Russian option with a finite time horizon. It is shown that the value of the Russian option solves a certain free boundary problem. This information is used to analyze the optimal stopping boundary.

A study of perpetual game options is performed in Paper IV. One of the main results provides a condition under which the value of the option is increasing in the volatility.

In Paper V options written on several underlying assets are considered. It is shown that, within a large class of models, the only model for the stock prices that assigns convex option prices to all convex contract functions is geometric Brownian motion.

Finally, in Paper VI it is shown that the optimal stopping boundary for the American put option is convex in the standard Black-Scholes model.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2004. 17 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 38
Mathematical analysis, American options, convexity, monotonicity in the volatility, robustness, optimal stopping, parabolic equations, free boundary problems, volatility, Russian options, game options, excessive functions, superreplication, smooth fit, Matematisk analys
National Category
Mathematical Analysis
urn:nbn:se:uu:diva-4574 (URN)91-506-1774-5 (ISBN)
Public defence
2004-10-29, 2146, Buliding 2, Polacksbacken, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 13:15
Available from: 2004-10-08 Created: 2004-10-08Bibliographically approved

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Ekström, Erik
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