# MATH3075/3975 Financial Mathematics

## General Information

This page contains information on the Senior mainstream Unit of Study MATH3075 Financial Mathematics and the Senior advanced Unit of Study MATH3975 Financial Mathematics (advanced). Note that MATH3075 and MATH3975 share the same classes.

- Taught in Semester 2.
- Credit point value: 6.
- Classes per week: Three lectures and one tutorial.
- Lecturer(s): Marek Rutkowski .

Please refer to the Senior Mathematics and Statistics Handbook for all questions relating to Senior Mathematics and Statistics. In particular, see the MATH3075/3975 handbook entry for further information relating to MATH3075 and MATH3975.

You may also view the description of MATH3075 and the description of MATH3975 in the central units of study database.

## Outline

- The aim of the course MATH3075/3975 is to give an introduction to the mathematical theory of modern financial markets with the emphasis on pricing and hedging of derivative securities. Topics covered by this course include: probability review, introduction to securities markets, the modelling of riskless and risky securities, the concept of arbitrage, the risk-neutral probabilities (equivalent martingale measures) and their applications, the fundamental theorem of asset pricing, the study of complete and incomplete market models, the pricing and hedging of options of European and American style, the put-call parity relationship, the binomial options pricing model and the CRR call option pricing formula, the Brownian motion, the Black-Scholes model and the derivation of the Black-Scholes call option pricing formula.
- Students enrolled in MATH3975 will also be required to get familiar with proofs of all results, including the Fundamental Theorem of Asset Pricing. In addition, they should understand the concept of a martingale and be able to examine the basic properties of martingales, as well as to analyse Markov and martingale properties of the (geometric) Brownian motion.

## Lectures

- Lectures in the normal unit MATH3075 will be held concurrently with those of the corresponding advanced unit MATH3975.
- It is highly recommended that you read the relevant part of the course notes before each lecture.

## Course Notes and Slides

Download lecture notes and slides (PDF files) here:

- Information: Sheet (updated)
- Information: Slides (updated)
- Course Notes 2016
- Slides 1: Probability Review (Chapter 6)
- Slides 2: Securities Markets (Chapter 1)
- Slides 3: Elementary Market Model (Chapter 2: Section 2.1)
- Slides 4: Single Period Models (Chapter 2: Section 2.2)
- Slides 5: Filtrations and Conditioning (Chapter 3: Sections 3.1.1-3.1.3)
- Slides 6: Multi-Period Markets (Chapter 3: Sections 3.1.4-3.1.9)
- Slides 7: Binomial Market Model (Chapter 4)
- MATH3975: Game Contingent Claims (Section 4.5)
- MATH3975: RBSDE and Options (optional lecture)
- J. F. Nash (1950)
- Slides 8: Black-Scholes Model (Chapter 5)

## Tutorial Problems and Solutions

Download tutorial problems and solutions (PDF files) here:

- Tutorials
- Week 2: Problems and Solutions
- Week 3: Problems and Solutions
- Week 4: Problems and Solutions
- Week 5: Problems and Solutions
- Week 6: Problems and Solutions
- Week 7: Problems and Solutions
- Week 8: Problems and Solutions
- Week 9: Problems and Solutions
- Week 10: Problems and Solutions
- Week 11: Problems and Solutions
- Week 12: Revision
- Week 13: Revision

## Equity Options (NYSE)

## DJIA Options (CBOE)

## Nasdaq 100 Options (NYSE)

## Crude Oil Futures and Options (NYMEX)

- Crude Oil Futures Contract
- Crude Oil Futures Settlement
- Crude Oil Futures Quotes
- Crude Oil Options
- Crude Oil Options Quotes (Aug-Sep)
- Crude Oil Options Quotes (Sep-Sep)

## Further readings (not compulsory):

- "Investigations on the Theory of Brownian Movement" by A. Einstein (1905)
- "Two-State Option Pricing" by R. Rendleman and B. Bartter (1979)
- "The Pricing of Options and Corporate Liabilities" by F. Black and M. Scholes (1973)
- "A Note on the Call-Put Parity and a Call-Put Duality" by G. Peskir and A.N. Shiryaev (2001)
- "The Origins of Risk-Neutral Pricing and the Black-Scholes Formula" by L.C.G. Rogers (2005)
- "P versus Q" by A. Meucci (2011)
- "Option Traders Use (Very) Sophisticated Heuristics, Never the Black-Scholes-Merton Formula" by E. Haug and N. Taleb (2011)
- "The Origins of the Word Martingale" by R. Mansuy (2005)
- "The Work of Kyosi Ito" by P. Protter (2006)
- "Efficient Markets, Random Paths" by H. Foellmer (2007)
- "Beyond Black-Scholes" by M. Haug (2010)
- "What is Mathematics For?" by U. Dudley (2010)

## Consultations during the study week

Marek Rutkowski is on leave from 26 October till 12 November.

## Unit Assessments: Semester 2, 2016

Assessment tasks for MATH3075 and MATH3975 are as follows:

- Two assignments worth 10% each = 20%
- Final examination on 10 November 2016, 9:20 am - 11:30 am, worth 80%.
- MATH3075 Recommended exercises for revision
- MATH3075 Examination guide
- MATH3975 Recommended exercises for revision
- MATH3975 Examination guide
- Assignment cover sheet

- Assignment 1 is now available here with submission either before or at the beginning of the lecture on Monday, September 5 (Week 7). Marks scale 0-20.
- Assignment 1 and MATH3075 Solutions and MATH3975 Solutions
- Assignment 2 is now available here with submission either before or at the beginning of the lecture on Monday, October 17. Marks scale 0-20.
- Assignment 2 and MATH3075 Solutions and MATH3975 Solutions

**Check your marks**

MATH3075 students: please check that your marks for Assignment (Quiz) 1 and Assignment (Quiz) 2 have been recorded correctly by pressing the "Check marks" button.

Please note that any corrections to Assignment (Quiz) 1 marks must be made by Friday, Sep 30.

Please note that any corrections to Assignment (Quiz) 2 marks must be made by Friday, Nov 04.

**Check your marks**

MATH3975 students: please check that your marks for Assignment (Quiz) 1 and Assignment (Quiz) 2 have been recorded correctly by pressing the "Check marks" button.

Please note that any corrections to Assignment (Quiz) 1 marks must be made by Friday, Sep 30.

Please note that any corrections to Assignment (Quiz) 2 marks must be made by Friday, Nov 04.

## Timetable

Show timetable / Hide timetable.