Syllabus/achievement requirements

Two relevant books (If you really want to buy one, I recommend [P] )

[P] S. Pliska. Introduction to Mathematical Finance. Discrete-Time Models. Blackwell Publishing.

[CZ] M. Capi¨½ski and T. Zastawniak. Mathematics for Finance. An Introduction to Financial Engineering.

The following is the syllabus for the course:

Sections 8 and 9 are NOT material for examination.

1. Introduction.
   1. Basic concepts of financial markets.
   2. Motivational examples for the use of derivatives.
2. Time value of the money. [CZ]
   1. Simple interest.
   2. Discrete or periodic compounding
   3. Continuous compounding.
   4. Comparing compounding methods.
   5. Streams of payments.
   6. Money market.
   7. Money market account.
3. Basic financial derivatives. [CZ]
   1. Forwards contracts.
      1. Forward price.
      2. Value of a forward contract.
   2. Futures
   3. Options.
      1. Put-call parity
      2. Bounds on option prices.
      3. Variables determining option prices.
         1. European options.
         2. American options.
      4. Time value of options.
      5. Hedging and speculating with options
         1. Bullish strategies.
         2. Bearish strategies.
         3. Neutral or non-directional strategies.
4. Single period market models. [P]
   1. Model specifications.
   2. Arbitrage and other economic considerations.
   3. Linear programming.
   4. Risk neutral probability measures.
   5. Valuation of contingent claims.
   6. Complete and incomplete markets.
5. Portfolio optimization in single period markets [P]
   1. Optimal portfolios and viability.
   2. Risk neutral computational approach.
6. Review of probability. [P]
   1. Information and measurability.
   2. Conditional expectation.
7. Multi-period securities markets. [P]
   1. Model specifications.
   2. Economic considerations.
   3. Risk neutral pricing.
   4. Complete and incomplete markets.
   5. Optimal portfolio problem.
      1. Martingale method.
8. The Cox-Ross-Rubinstein model.
   1. Introduction.
   2. Bernoulli processes and related processes.
   3. The Cox-Ross-Rubinstein model.
   4. Pricing European options in the CRR model.
   5. Hedging European options in the CRR model.
9. The Black-Scholes model.
   1. Introduction.
   2. Brownian motion and related processes.
   3. The Black-Scholes model.
   4. The Black-Scholes pricing formula.
   5. Convergence of the CRR pricing formula to the Black-Scholes pricing formula.