AMAT 31303 : Mathematics for Finance I

Course Code : AMAT 31303

Title               :  Mathematics for Finance I

Pre-requisites   : PMAT 21272

Learning outcomes :

At the end of the course candidate will be able to

• define time value of money

• calculate present and future values of annuities and cash flows

• construct an investment portfolio to match present value and duration of a set of liability cash flows

• define basic types of financial derivatives

• identify appropriate derivative position for given investment circumstances

• evaluate the payoff and profit of basic derivative contracts

• apply put-call parity to identify arbitrage opportunities

Course Contents:

Interest Theory: Time Value of Money: 

• Simple, compound Interest, comparing simple and compound interest, accumulation function, future value, current value, present value, net present value, discounting discount factor, rate of discount, interest payable monthly, quarterly, etc., nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value.

Annuities/cash flows: 

• Annuity-immediate, annuity due, perpetuity, payable monthly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity.

Loans: 

• Principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund.

Bonds: 

• Price, book value, amortization of premium, accumulation of discount, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, callable/non-callable.

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, margin, 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, properties of stock options, factors affecting option prices, assumptions and notations, 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.

Method of Teaching and Learning: A combination of lectures, tutorial discussions, industrial presentations, seminars

Assessment :  Based on tutorials, quizzes, mid-term tests and end of course examination

Recommended Readings:

1. Kellison, S. (3 rd Ed., 2008). The Theory of Interest, McGraw-Hill/Irwin.

2. Hull, J.C. (10th Ed., 2018). Options, Futures and Other Derivatives, Pearson.

3. McDonald, R.L. (3 rd Ed., 2013). Derivatives Markets, Addison Wesley.

4. Kosowski, R. & Neftci, S.N. (3 rd Ed., 2015). Principles of Financial Engineering, Academic Press