AMAT 41403: Financial Mathematics

Course Code : AMAT 41403

Title               : Financial Mathematics

Pre-requisites : PMAT 21272

Learning outcomes:

On successfully completion of the course the student 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

• evaluate the payoff and profit of basic derivative contracts

• apply put-call parity to identify arbitrage opportunities

• calculate the option price on various underlying assets using Binomial tree method

• solve Black-Scholes equation numerically

• define appropriate Swap strategies.

Course Content:

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.

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.

Option Pricing using Binomial Trees: 

• A one-step binomial model and a no-arbitrage argument, Risk-neutral valuation, Two-step binomial trees, Put and Call options, American options, Delta, Matching volatility with u and d, binomial tree formulas, increasing the number of steps, create spreadsheet application

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.

Swaps: 

• Swap, swap term, prepaid swap, notional amount, swap spread, deferred swap, simple commodity swap, interest rate swap

Assessment: A combination of lectures, tutorial discussions and presentations

Recommended Readings:

1. Kellison, S. (3rd 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. (3rd Ed., 2013). Derivatives Markets, Addison Wesley.

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