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
- define and recognize the definitions of the financial derivatives
- calculate the option pricing on various underlying assets
- solve Black-Scholes equation numerically
- identify the Greeks and their use
- 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:
- John C Hull, Options, Futures and Other Derivatives (10e), Pearson, 2017
- McDonald, R.L., Derivatives Markets, Addison Wesley, 2013
- Robert Kosowski, Salih N. Neftci, Principles of Financial Engineering, Academic Press, 2014