Arbitrage Pricing

Prerequisites

Statistics, Financial Econometrics

Objectives

Arbitrage Pricing develops the notion of ‘no-arbitrage’ or ‘no free lunch’ from first principles. After having taken the course, students will be familiar with the general concept of no-arbitrage, and its use in the pricing of uncertain cash flows with common models used in the industry and academia.

Description / Program

The course is structured along the following topics.

• Brief review of probability
• No-arbitrage in the static, finite-dimensional case
• No-arbitrage in a dynamic (in)finite-dimensional setting
• Brownian motion
• Introduction to the stochastic calculus
• Feynman-Kac theorem
• Black-Scholes model
• (Affine) term structure models

Learning Method / Style of Lessons

Our classes will simultaneously develop the theory and its applications. Students will be introduced to the must-know models for a career in modeling and pricing.

Compliant with COVID-19 guidelines.

Exam Style

Weekly homeworks will account for 40% of the grade, a final written exam for  60%.

Requested Material

All material will be provided.

Readings/Textbooks

We will be developing all the material autonomously. Relevant textbooks that may help are

Bjork, T. (1998). Arbitrage Theory in Continuous Time. Oxford University Press.

Brigo, D. and Mercurio, F. (2006). Interest Rate Models – Theory and Prac- tice. With Smile, Inflation and Credit. Springer Finance. Springer-Verlag, 2nd edition.

Øksendahl, B. (2000). Stochastic Differential Equations. Springer.

Shreve, S. E. (2004). Stochastic Calculus for Finance II, Continuous-Time Models. Springer, Berlin