Intended Schedule

Note that the lecture numbers and contents can change without notice.

  1. Money: The Zero Coupon Bond.
  2. Bond portfolios and immunization.
  3. Instruments: Stocks, Derivatives (mainly Options).
  4. Prediction and Trading.
  5. Measures of trading performance. Ex-post optimal trading
  6. Arbitrage and the Martingale Measure.
  7. Proof of the positive supporting price theorem.
  8. The risk neutral world and expectations.
  9. Binomial models for geometric Brownian stock dynamics.
  10. Pricing using Martingale measures in binomial models.
  11. Monte Carlo methods for pricing almost arbitrary derivatives.
  12. Path Generation in Monte Carlo Methods.
  13. Introduction to Monte Carlo.
  14. Variance reduction
  15. Importance sampling and low discrepancy sequences.
  16. Analytic pricing: The European options; barrier options.
  17. Stochastic Calculus.
  18. The PDE approach.
  19. The American Put option: Dynamic programming on the binomial tree.
  20. The American Put option: LeastSquaresMethod and OPTimal for finding the exercise boundary. Backward path generation, efficiency and memory issues.
  21. Pricing the American Put by optimizing bounds.
  22. Estimating and predicting parameters in the stock price dynamics: Maximum likelihood; Cross Entropy; ARCH and GARCH.
  23. Portfolio Optimization: mean-variance analysis.
  24. Portfolio optimization as Mixed Integer Linear Programs (MILPs).
  25. Value at Risk (VAR) and evaluation of loan portfolios.
  26. Monte Carlo estimates of rare event probabilities.
  27. Auctions.
  28. Distributed ledgers and digital currency -- BitCoin