Syllabus/achievement requirements

Main textbook:

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

For the topics not covered in [P], I will upload my notes to the webpage of the course.

Part I (Lecture notes on the course¡¯s webpage)

1. Introduction.
   1. Basic concepts of financial markets.
   2. Motivational examples for the use of derivatives.
2. Time value of the money.
   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.
   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.

Part II ([P] Sections 1.1-1.5, 2.1-2.2.)

4. Single period market models.
   1. Model specifications.
   2. Arbitrage and other economic considerations.
   3. Linear programming. (Handwritten notes on the course¡¯s webpage)
   4. Risk neutral probability measures.
   5. Valuation of contingent claims.
   6. Complete and incomplete markets.
5. Portfolio optimisation in single period markets
   1. Optimal portfolios and viability.
   2. Risk neutral computational approach.

Part III  ([P] Sections 3.1,3.3-3.4, 4.1, 5.1-5.2.)

6. Review of probability. (Handwritten notes on the course¡¯s webpage)
   1. Information and measurability.
   2. Conditional expectation.
7. Multi period securities markets.
   1. Model specifications.
   2. Economic considerations.
   3. Risk neutral pricing.
   4. Complete and incomplete markets.
   5. Optimal portfolio problem.
      1. Martingale method.

Part IV (Slides on the course¡¯s webpage)

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.
10. Convergence of the CRR pricing formula to the Black-Scholes pricing formula.