AMAT 32343 : Mathematics for Finance II

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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.
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