## MST30030: Financial Mathematics

### Lecturer: Masha Vlasenko

The ultimate goal of this course is to introduce students to the Black-Scholes Model for options pricing. The module opens by looking at various types of options and discussing their properties. The technique of constructing binomial trees to price options (based on the Cox, Ross and Rubenstein paper of 1979) is then discussed in detail. We then study the model of stock price behaviour introduced by Black, Scholes and Merton in 1973, and derive the Black-Scholes model for valuing European call and put options on a non-dividend-paying stock. A brief introduction to probability theory is included in the course.
Our main textbook is John C. Hull, "Options, Futures and Other Derivatives".

FINAL EXAM took place on Saturday, December 14: [paper], [solutions], grading scheme
Sample exam [paper] and [solutions]. See the last pages of lecture notes for the information on this year's exam questions.

Continuous assessment marks are here.

• Lecture 1: Financial Derivatives [pdf]
• Lecture 3: Interest Rates [pdf]
• Lecture 4: Properties of Stock Options [pdf]
• Lecture 5: Put-Call Parity [pdf]
• Lectures 6-7: Axioms of Probability Theory -- Discrete Models
• Lectures 8-10: Axioms of Probability Theory -- Continuous Models
[pdf]
• Lecture 11: Conditional Probability
• Lecture 12: Stochastic Independence
• Lecture 13: Random Variables
• Lecture 14: Binomial Distribution
• Lecture 15: Normal Distribution
[pdf]
• Lecture 16: Delta Hedging [pdf]
• Lecture 17: Binomial Tree Model for Option Pricing [pdf]
• Lecture 18: Stochastic Processes and Brownian Motion
• Lectures 19-20: Stochastic Models for Stock Market
[pdf]
• Lectures 21-22: Black-Scholes Formula for Option Prices [pdf]
• Lectures 23-24: Black-Scholes-Merton Differential Equation [pdf]

### Assessment

• 30% continuous assessment
• 70% final exam