Syllabus

Title
4587 Y1P4 Continuous Time Finance 1
Instructors
Christa Cuchiero, Ph.D.
Contact details
Type
PI
Weekly hours
2
Language of instruction
Englisch
Registration
02/05/19 to 02/24/19
Registration via LPIS
Notes to the course
Subject(s) Master Programs
Dates
Day Date Time Room
Tuesday 05/14/19 09:00 AM - 01:00 PM TC.3.05
Tuesday 05/21/19 09:00 AM - 01:00 PM TC.3.05
Tuesday 05/28/19 09:00 AM - 01:00 PM TC.3.05
Tuesday 06/04/19 09:00 AM - 01:00 PM TC.3.05
Tuesday 06/11/19 09:00 AM - 01:00 PM TC.3.05
Tuesday 06/18/19 09:00 AM - 01:00 PM TC.3.21
Friday 06/21/19 09:00 AM - 11:00 AM TC.0.04

Contents

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

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.

Attendance requirements

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

Teaching/learning method(s)

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

Assessment

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).

Prerequisites for participation and waiting lists

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

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

.

Readings

1 Author: Rüdiger Frey
Title: Lecture Notes Continuous Time Finance, Chapter 1-4

Publisher: available from http://statmath.wu.ac.at/~frey/lecture_notes.htm
Content relevant for class examination: Yes
Type: Script
2 Author: Bjoerk Thomas
Title: Arbitrage theory in Continuous Time

Content relevant for class examination: No
Content relevant for diploma examination: No
Recommendation: Reference literature
Type: Book
3 Author: Shreve, Stephen
Title: Stochastic Calculus for Finance II: Continuous Time Models

Content relevant for class examination: No
Content relevant for diploma examination: No
Recommendation: Strongly recommended (but no absolute necessity for purchase)
Type: Book
4 Author: Berndt Oksendal
Title:

Stochastic Differential Equations, An Introduction with Applications


Content relevant for class examination: No
Recommendation: Reference literature
Type: Book

Recommended previous knowledge and skills

Probability and Mathematics II from QFin or equivalent

Last edited: 2019-05-08



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