Kaisa_2012_3_photo by Veikko Somerpuro

Contents

We will learn to apply powerful concepts and techniques from stochastic analysis for pricing and hedging financial derivatives.

1. American options and optimal stopping strategies in discrete time.
2. Black & Scholes continuous time model as limit of time-discrete Cox-Ross-Rubinstein binomial tree model.
3. Brownian motion. Introduction to stochastic integration and Ito calculus. Ito-Föllmer pathwise integral.
4. ABC of Malliavin calculus and Ito-Clark-Ocone representation formula.
5. Option pricing and hedging in the continuous Black & Scholesin market model. Black & Scholes Partial Differential Equation.
6. Modeling interest rates and bond markets.

Ilmoittaudu
23.10.2017 klo 09:00 - 13.12.2017 klo 23:59

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ma 30.10.2017
10:15 - 12:00
Ti 31.10.2017
12:15 - 14:00
Ma 6.11.2017
10:15 - 12:00
Ti 7.11.2017
12:15 - 14:00
Ma 13.11.2017
10:15 - 12:00
Ti 14.11.2017
12:15 - 14:00
Ma 20.11.2017
10:15 - 12:00
Ti 21.11.2017
12:15 - 14:00
Ma 27.11.2017
10:15 - 12:00
Ti 28.11.2017
12:15 - 14:00
Ma 4.12.2017
10:15 - 12:00
Ti 5.12.2017
12:15 - 14:00
Ma 11.12.2017
10:15 - 12:00
Ti 12.12.2017
12:15 - 14:00
Pe 15.12.2017
09:15 - 12:00

Muu opetus

02.11. - 14.12.2017 To 10.15-12.00
Dario Gasbarra
Opetuskieli: englanti

Materiaalit

Bibliography:

Jamil Baz & George Chacko : Financial Derivatives, Pricing Applications and Mathematics, Cambridge 2009.

Tomas_Bjork: Arbitrage Theory in Continuous Time, Oxford_Finance 2009.

Bruno Bouchard & Jean-Francois Chassagneux: Fundamentals and Advanced Techniques in Derivative Hedging, Springer 2016.

Yuliya MIshura: Financial Mathematics. ISTE Press & Elsevier 2016

Sottinen: Rahoitusteoria 2006.

Dieter Sondermann: Introduction to Stochastic Calculus for Finance, A New Didactic Approach, Springer Lecture Notes in Economics and Mathematical Systems (2007)

Tehtävät

Kuvaus

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

Probability theory I,II, and their prerequisites

Stochastic analysis

Option pricing in continuous time

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Financial markets in continuous time. Black and Scholes formula. Incomplete market models. Interest rate models.

Lecture notes; Baz & Chacko: Financial Derivatives

Exam, other methods will be described later