Course Code : AMAT 32633

Title : Mathematics for Finance II

Pre-requisites: AMAT 31603

Learning outcomes: On successfully completion of the course the student will be able to

1. define and recognize the definitions of the financial derivatives

2. calculate the option pricing on various underlying assets

3. solve Black-Scholes equation numerically

4. identify the Greeks and their use

5. identify Swap strategies

Course Contents:

Trading Strategies: Single option and stock, Spreads and Combinations, Box spreads, Butterfly spreads,

Option Pricing: Binomial Trees: One, two or more binomial periods, Put and Call options, American options, Options on stock index, currencies and future contracts, Risk Neutral pricing, log normality. The Black-Scholes Formula: Brownian motion, martingales, stochastic calculus, Ito processes, stochastic models of security prices, Black-Scholes Merton Model, Black-Scholes Pricing formula on call and put options, Applying formula to other assets.

Numerical Solutions to Black-Scholes Equation: Converting to parabolic type, Finite difference methods, FTCS, BTCS and Cranck-Nicholson Schemes for Black-Scholes Equation

Option Greeks: Definition of Greeks, Greek Measures for Portfolios.

Swaps: swap, swap term, prepaid swap, notional amount, swap spread, deferred swap, simple commodity swap, interest rate swap

Method of Teaching and Learning : A combination of lectures and tutorial discussions

Assessment : Based on tutorials, tests and end of course examination

Recommended Readings:

1. John C Hull, Options, Futures

2. McDonald, R.L., Derivatives Markets, Addison Wesley, 2013

3. Robert Kosowski, Salih N. Neftci, Principles of Financial Engineering, Academic Press, 2014