Course Code : AMAT 41813
Title : Financial Mathematics
Pre-requisites : PMAT 11522
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 Content:
Time Value of Money: Simple and Compound Interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate (rate of discount), convertible monthly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value.
General Cash Flows and Portfolios: yield rate/rate of return, dollar-weighted rate of return, time weighted rate of return, current value, duration (Macaulay and modified), convexity (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, stock price, stock dividend
Basic terms in Financial Markets: derivative, underlying asset, over the counter market, short selling, short position, long position, ask price, bid price, bid-ask spread, lease rate, stock index, spot price, net profit, payoff, credit risk, dividends, mmargin, maintenance margin, margin call, mark to market, no arbitrage, risk-averse, type of traders.
Options: call option, put option, expiration, expiration date, strike price/exercise price, European option, American option, Bermudan option, option writer, in-the-money, at-the-money, out-of-the-money, covered call, naked writing, put-call parity.
Forwards and Futures: forward contract, futures contract, outright purchase, fully leveraged purchase, prepaid forward contract, synthetic forwards, cost of carry, implied repo-rate.
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.
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
Assessment: Based on assignment, quizzes, group projects, mid-term test, 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