Introduction to Quantitative Finance

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The aim of this course is to acquaint students with the fundamental theories in Quantitative Finance. The theories set out to analyze the complexity of options and their underlying price processes. Given that future prices are a set of many possibilities, and the ultimate outcome is random, we will learn mathematical tools to help distinguish the many probable economic states, which provides a price mechanism. The Black-Scholes Formula for option pricing, will derive in to gain the mathematical skills and economic insight which are needed to succeed in the field.

1) Introduction to Options and other Financial Instruments

2) Future – Present Value Lemma

3) Binomial Model

4) Martingale Theory

5) Brownian Motion

6) Stochastic Calculus

7) Ito’s Lemma

8) Risk Neutral Valuation

9) Change of Numeraire

10) Girsanov’s Theorem

11) Transformation of SDE to PDE method: Feynman-Kac Stochastic Representation

12) Derivations of Black-Scholes Formula

13) Other Stochastic Differential Equations

14) Introduction to Fractional Brownian Motion

Basic

Hull, J. C. - Options Futures, and Other Derivatives

Etheridge, A. - A Course in Financial Calculus

Baxter, M., & Rennie, A. - Financial Calculus: An Introduction to Derivative Pricing.

Black, F. & Scholes, M. (1973) The pricing of options and corporate liabilities. The journal of political economy, 81(3), 637-654.

Shreve, S. E. - Stochastic Calculus for Finance I I: The Binomial Asset Pricing Model

Neftci, S. N. - An Introduction to the Mathematics of Financial Derivatives

Advance

Shreve, S. E. - Stochastic Calculus for Finance II: Continuous-Time Models

Karlin, S. and Taylor H. M. - A First Course in Stochastic Processes

Øksendal, B. Stochastic differential equations. In Stochastic differential equations

The student will understand the mathematical foundations of Quantitative Finance.

With this knowledge the student will be able to understand and explain the underlying economic and mathematical principles which will permit him to apply the models on his own.

The acquired skills will permit the student to analyze prices processes and distinguish the most probable economic states which will prevail in the future.

Final exam 70%

Homework 30% submitted on time and in pairs