MAS362/462/6053 Financial Mathematics 2016-2017

Lecturer: Dr M. Katzman




The Syllabus

  1. Interest rates, bonds and yield curves. (2 lectures)
  2. Forward and Futures contracts. (3 lectures)
  3. Options. (3 lectures)
  4. Binomial trees and risk neutral valuation. (3 lectures)
  5. The stochastic process followed by stock prices. (2 lectures)
  6. The Black-Scholes pricing formulas. (2 lectures)
  7. Portfolio theory. (2 lectures)
  8. The Capital Asset Pricing Model. (3 lectures)

A pdf version of the syllabus is here.

A summary of the material in the course


Lectures' slides

Printable format

Prologue Interest rates Forward and future contracts Options
Binomial trees and risk-neutral valuation The stochastic process followed by stock prices  The Black-Scholes pricing formulas  Portfolio Theory 
The Capital Asset Pricing Model

A review of probability.


Homework Assignments

I will assign problems periodically.

Homework #1 Due on Monday,  October 16th. Hand in #4, 5, 6.
Homework #2  Due on Monday,  October 30th. Hand in #2, 3, 5.
Homework #3 Due on Monday,  November 13th. Hand in #1, 2, 3.
Homework #4  Due on Wednesday, November 29th. Hand in #1, 4, 6 ,7.
Homework #5


MAS462 Project

MAS6053 Project



The Exam

You will be asked to answer 4 questions out of 4 (no choice).

The exam will cover all the material taught in the course. You should expect to see problems similar to the examples discussed in class and to the homework problems. You are expected to know how to prove all statements proved in lecture except for the following:

  1. The informal proof of Ito's Lemma, however, you will be expected to know its statement.
  2. Computing Ito integrals from first priciples, i.e., as limits of sums of random variables.
  3. You dont need to memorize the exact form of the Black-Scholes PDE, HOWEVER,  you will be expected to know its significance, and you will be expected to know how it is derived.
  4. The Black-Scholes pricing formulas, however, you will be expected to know their significance.
  5. The proof of Theorem 8.1
Recent past exams can give you some idea of the kind of questions you might see in this year's exam..

Past Exams

2012-13 exam and its solution. 
2013-14 exam and its solution.
2014-15 exam and its solution.
2015-16 exam and its solution.
2016-17 exam and its solution.

Glossary of financial terms from Wikipedia (correct last time I checked...)

Bond Yield curve
Stock Option
Futures contract Forward contract
Brownian motion Black-Scholes
Modern portfolio theory Capital asset pricing model


Useful links


Robert Shiller, one of the world's top economists, has made available online his course "Financial markets". You can watch videos of all the lectures here. Any students interested in Finance and Economics will benefit greatly from these very well delivered lectures. In particular, for MAS362 students this is a chance to learn the non-mathematical, real-life context of much of the material taught in the course. Highly recommended!

Exchanges Market Data            
The London Stock Exchange Chicago Mercantile Exchange
LIFFE (International Financial Futures and Options Exchange)       ADVFN
New York Mercantile Exchange Interactive Investor
New York Stock Exchange RiskMetrics
Standard & Poor's Wilmott


Black-Scholes on TV and on the radio!

FT's John Authers on Volkswagen's short squeeze

Negative risk-free returns? See John Authers on Impossibilities in the markets and New York Times' Investors Buy U.S. Debt at Zero Yield.  

Life without a risk-free benchmark 

How logic can lead to a crisis (How many flaws can you find in this argument against CAPM?)

The mathematical equation that caused the banks to crash

Dreaming of being a fat cat?

You can look for finance job ads in and in

Most positions require experience and/or postgraduate degrees but there are occasional positions where no experience is required.