AMAT 32343 : Mathematics for Finance II

Course Code  : AMAT 32343

Title         : Mathematics for Finance II

Pre-requisites : AMAT 31303

Learning outcomes:

On successfully completion of the course the student will be able to

• derive the payoff/profit diagrams for given trading strategy

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

• solve Black-Scholes equation numerically

• identify the Greeks and their use

• define appropriate Swap strategies.

Course Contents:

Trading Strategies: 

• Single option and stock, Spreads: Bull spread, Bear Spread, Box spreads, Butterfly spreads and Combinations: Straddle, Strips and Straps.

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.

Numerical Solutions to Black-Scholes Equation: 

• Converting to parabolic type, Finite difference methods, FTCS, BTCS and Crank-Nicholson Schemes for Black-Scholes Equation, implement the various numerical schemes using an appropriate software.

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

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

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