Syllabus

Titel
4587 Y1P4 Continuous Time Finance 1
LV-Leiter/innen
Christa Cuchiero, Ph.D.
Kontakt
  • LV-Typ
    PI
  • Semesterstunden
    2
  • Unterrichtssprache
    Englisch
Anmeldung
05.02.2019 bis 24.02.2019
Anmeldung über LPIS
Hinweise zur LV
Planpunkt(e) Master
Termine
Wochentag Datum Uhrzeit Raum
Dienstag 14.05.2019 09:00 - 13:00 TC.3.05
Dienstag 21.05.2019 09:00 - 13:00 TC.3.05
Dienstag 28.05.2019 09:00 - 13:00 TC.3.05
Dienstag 04.06.2019 09:00 - 13:00 TC.3.05
Dienstag 11.06.2019 09:00 - 13:00 TC.3.05
Dienstag 18.06.2019 09:00 - 13:00 TC.3.21
Freitag 21.06.2019 09:00 - 11:00 TC.0.04

Inhalte der LV

This lecture discusses the basic mathematical tools for continuous-time finance and applies these to problems in derivative pricing. In particular we study option pricing in the Black Scholes model.

We will cover the following topics

  • Wiener process and compound Poisson processes
  • Quadratic variation
  • Pathwise Ito calculus, elementary Ito integral and the Ito formula
  • Generators and Feynman Kac for one-dimensional diffusions
  • Derivative pricing via replication in the Black Scholes model
  • Black Scholes formula and application
  • Extensions beyond the classical Black Scholes model
  • Basic numeric approaches for option pricing

Lernergebnisse (Learning Outcomes)

Continuous time finance is concerned with: Brownian motion, stochastic calculus, risk-neutral pricing, stochastic and partial differential equations, exotic options.

After completing this class the student will have the ability to:

• describe the basic concepts and methods of continuous time finance;

• apply and do computational work with the basic concepts and definitions of continuous time finance.

After completing this class the student will also have the ability to:

• confidently apply ideas of continuous time finance in doing analytical work for financial markets.

• solve applied problems where skills are required from continuous time finance.

Regelung zur Anwesenheit

Standard rules for PIs (80 % of lectures and tutorium)

Lehr-/Lerndesign

This class is taught as a lecture complemented with exercises and a tutorium

Leistung(en) für eine Beurteilung

Midterm Exam (20%)

Exercise Series (25%)

Final exam (55%)

A minimum score of 40% in the final exam and an overall score of 50 % is necessary for passing.

Exercises will be discussed during the tutorium (also additional exercises).

Teilnahmevoraussetzung(en) und Vergabe von Wartelistenplätzen

• Advanced Business Mathematics (class Mathematics I of the QFin program);

• Advanced Business Probability theory (class Probability of the QFin program);

.

Literatur

1 Autor/in: Rüdiger Frey
Titel: Lecture Notes Continuous Time Finance, Chapter 1-4

Verlag: available from http://statmath.wu.ac.at/~frey/lecture_notes.htm
Prüfungsstoff: Ja
Art: Skriptum
2 Autor/in: Bjoerk Thomas
Titel: Arbitrage theory in Continuous Time

Prüfungsstoff: Nein
Diplomprüfungsstoff: Nein
Empfehlung: Referenzliteratur
Art: Buch
3 Autor/in: Shreve, Stephen
Titel: Stochastic Calculus for Finance II: Continuous Time Models

Prüfungsstoff: Nein
Diplomprüfungsstoff: Nein
Empfehlung: Stark empfohlen (aber nicht absolute Kaufnotwendigkeit)
Art: Buch
4 Autor/in: Berndt Oksendal
Titel:

Stochastic Differential Equations, An Introduction with Applications


Prüfungsstoff: Nein
Empfehlung: Referenzliteratur
Art: Buch

Empfohlene inhaltliche Vorkenntnisse

Probability and Mathematics II from QFin or equivalent

Zuletzt bearbeitet: 08.05.2019



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