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:
- Hull, J.C. (10th Ed., 2018). Options, Futures and Other Derivatives, Pearson.
- McDonald, R.L. (3rd Ed., 2013). Derivatives Markets, Addison Wesley.
- Kosowski, R. & Neftci, S.N. (3rd Ed., 2015). Principles of Financial Engineering, Academic Press.