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Continuous Time Quantitative Finance

Lecturer: Prof. Dr. Marc CHESNEYLocation: PLM-1-103/104Time: Mo 13.00 15:45

First lecture: 22.02.2010Language: English

Contents: Black and Scholes option pricing theory and changes of probability American options and hitting times Stochastic volatility models Its formula and Girsanov theorem for jump-diffusion processes The pricing of options in presence of possible discontinuities Exotic options Transaction costs Real Options

Description of the course:

The course focuses on the theoretical foundations of modern derivative pricing. Itaims at deriving option pricing models by relying on the main mathematical tools ofcontinuous time finance. A particular focus on jump processes is given. In light of therecent crisis, the introduction of possible financial crashes in financial modelling isnow essential and a clear understanding of Poisson processes is therefore important. Astandard background in stochastic calculus is required.

The last part of the course covers real options. Basic and recent models will bepresented. These include the introduction of competition and incomplete informationinto the real options framework. The use of the Real Options approach inEnvironmental Finance will also be presented.

Grades: The final grades will be based on a written or oral examination.

Literature:1. BERTOIN J.

Levy ProcessesCambridge University press, 2005

2. CONT R. and TANKOV P.Financial Modelling with Jump ProcessesChapman & Hall 2004

3. DANA, R.A. and JEANBLANC M.Marchs financiers en temps continu, valorisation et quilibreEconomica, 1994

4. DIXIT A. and R. PINDYCKInvestment under Uncertainty

Princeton University Press, 1994

5. DUFFIE D.Dynamic Asset Pricing TheoryPrinceton University Press, 2001

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6. DUMAS B. and ALLAZ B.

Les Titres Financiers : Equilibre du March et Mthodes dEvaluationP.U.F., 1995

7. ELLIOTT R.and KOPP E.Mathematics of Financial MarketsSpringer Finance, 2004

8. HULL J.Options, Futures and Other Derivative SecuritiesPrentice Hall, 2000

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10.JEANBLANC M., YOR M. and M. CHESNEYMathematical Methods for Financial MarketsSpringer Verlag, 2009

11.KARATZAS I. and SHREVE S.Brownian Motion and Stochastic CalculusSpringer Verlag

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13.MERTON R.Continuous Time FinanceBasic Blackwell, 1990

14. PROFETA C., ROYNETTE B. and M. YOROption prices as probabilitiesSpringer Verlag 2010

15.REVUZ D. and YOR M.Continuous Martingale and Brownian MotionSpringer Verlag, third edition, 1999

16.SANDMANN K.Einfhrung in die Stochastik der FinanzmrkteSpringer Verlag, 1999

17.TRIGEORGIS L.Real OptionsMIT Press, 1998

18.WILMOTT P.Derivatives : The Theory and Practice of Financial EngineeringJohn Wiley, 2000

19.ZAGST R.Interest Rate Risk ManagementSpringer Verlag, 2002