## Stochastic Analysis and Mathematical Finance – Summer Term 2018

On this webpage, you find all information pertaining to my course on **Stochastic Analysis and Mathematical Finance** held in the summer term 2018 at the University of Trier.

**General Information**

The **lectures** take place on

**Monday, 10:15 – 11:45 in HS 8.****Tuesday, 10:15 – 11:45 in HS 8.****Wednesday, 12:15 – 13:45 in E 50.**

The **exercise classes** take place on

**Monday, 15:45 – 17:15 in E 44.**

Exercise sheets are generally uploaded every Wednesday and are due on Wednesday at 13:45 of the following week. You can submit your solutions in **groups of 2-3** in the post box E14 on the ground floor of building E.

**Oral Exams**

To qualify for the final exam, you are required to attain **at least 50% of the points** on the exercise sheets and be able to demonstrate in the exercise classes that you have fully understood the solutions that your group has handed in. The dates for the exams are

**Monday, July 30, 2018****Friday, October 19, 2018**

Please register for the exam both with Ms. Karpa (E 113) as well as through Porta.

**Lecture Notes and Slides**

The course will follow the excellent lecture notes of **Prof. Frank Seifried**. The notes can be downloaded via the following link:

**Lecture Notes by Prof. Seifried**(Password Protected)

The lecture notes for my course on **Stochastic Processes** can be downloaded here:

Finally, the slides presented during the lectures can be downloaded here:

**Exercise Sheets**

The exercise sheets can be downloaded here:

**Exercise Sheet 01**: Financial Engineering, Put-Call Parity for Binary Options, Arbitrage, and Arbitrage Bounds.**Exercise Sheet 02**: The Binomial and Trinomial Market Models.**Exercise Sheet 03**: Arbitrage-Free Pricing, the Ask Price, and Stieltjes Integration.**Exercise Sheet 04**: Integration by Parts and Local Martingales.**Exercise Sheet 05**: Predictable Sigma-Field, Quadratic Covariation, Wiener Integrals, and Bounded Convergence for Stochastic Integrals.**Exercise Sheet 06**: Itô’s Formula, Ornstein-Uhlenbeck Dynamics, and Harmonic Functions.**Exercise Sheet 07**: Cholesky Decomposition of Brownian Motion, Computation of Equivalent Martingale Measures, Martingale Representation, and the CIR Process.

**Simulations**

**QuadraticVariationBM.m**: Discretized Total Variation (black) and Quadratic Variation (red) of a Brownian Motion (blue).

**QuadraticVariationStochInt.m**: Discretized Total Variation (black) and Quadratic Variation (red) of a stochastic Integral (blue) of a Fractional Brownian Motion (blue dotted) integrated with respect to a Brownian Motion. Requires the function **fbm1d**.

**SimpleIntegral.m**: Stochastic Integral (red) of a Simple Integrand (black) with respect to a Brownian Motion (blue).

**Implied Volatility**: Implied Volatilities of European Call Options on the S&P500 Index.