Continuous Time Finance (Summer Semester 2024)
- Lecturer: Prof. Dr. Vicky Fasen-Hartmann
- Classes: Lecture (0159400), Problem class (0159410)
- Weekly hours: 4+2
| Schedule | ||
|---|---|---|
| Lecture: | Tuesday 9:45-11:15 | 20.30 0.019 |
| Wednesday 8:00-9:30 | 20.30 0.014 | |
| Problem class: | Thursday 14:00-15:30 | 20.30 -1.012 |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | Prof. Dr. Vicky Fasen-Hartmann | |
| Office hours: On appointment. | ||
| Room 2.053 Kollegiengebäude Mathematik (20.30) | ||
| Email: vicky.fasen@kit.edu | Problem classes | Dr. Tamara Göll |
| Office hours: By arrangement | ||
| Room 2.014 Kollegiengebäude Mathematik (20.30) | ||
| Email: tamara.goell@kit.edu | ||
Content
The lecture deals with various central topics of financial mathematics in continuous time.
The contents of the lecture are split into two parts. The first part consists of an introduction to stochastic analysis. First, Brownian motion, the central stochastic process of the lecture, is introduced and important results from martingale theory are discussed. Afterwards, the stochastic integral is derived, various properties are shown and its central importance in financial mathematics is presented.
In the second part of the lecture, the focus will be on analyzing the Black-Scholes financial market. Here the share price is described by a geometric Brownian motion. It will be shown how options can be priced and hedged in such a market. Corresponding fundamental theorems for the Black-Scholes market are formulated, which establish relationships between absence of arbitrage, equivalent martingale measures and completeness. Finally, portfolio optimization and interest rate structure models are discussed.
Prerequisites
The lecture requires knowledge of the basics probability theory as taught in the lecture "Probability Theory" ("Wahrscheinlichkeitstheorie"). The lecture "Financial Mathematics in Discrete Time" ("Finanzmathematik in diskreter Zeit") is helpful, but is not a prerequisite.
Oral Exam
We will offer 2-3 examination dates during the lecture-free period. These will be set in the first weeks of lectures.
References
- Bäuerle (2013). Finanzmathematik in stetiger Zeit: Vorlesungsskript. KIT.
- Bingham & Kiesel (2004). Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives. Springer.
- Delbaen & Schachermayer (2006). The Mathematics of Arbitrage. Springer.
- Jeanblanc, M., Yor M. & M. Chesney (2009). Mathematical Methods for Financial Markets. Springer.
- Karatzas & Shreve (2000). Brownian Motion and Stochastic Calculus. Springer.
- Karatzas & Shreve (1998). Methods of Mathematical Finance. Springer.
- Klebaner, F.C. (2005). Introduction to stochastic calculus with applications. Imperial College Press.
- Korn & Korn (2009). Optionsbewertung und Portfolio-Optimierung. Vieweg+Teubner.
- Musiela & Rutkowski (2005). Martingale Methods in Financial Modelling. Springer.
- Mürmann, M. (2014). Wahrscheinlichkeitstheorie und Stochastische Prozesse. Springer.
- Øksendal (2000). Stochastic Differential Equations. Springer.
- Protter (2005). Stochastic Integration and Differential Equations. Springer.
- Revuz & Yor (2005). Continuous Martingales and Brownian Motion. Springer.
- Rogers & Williams (2000). Diffusions, Markov Processes and Martingales. (Volume 1 + 2) Cambridge University Press.
- Shreve (2004). Stochastic Calculus for Finance II. Springer.
- Steele, M. (2001). Stochastic calculus and financial applications. Springer.