### COURSE COVERAGE

Date | Coverage | Homework |
---|---|---|

Review | [review handout] | |

Jan.8 | Binomial model. Probability, sigma-fields, random variables,
expectation.
[lecture notes] |
[problem set 1] - hand in questions 4,5, and
9.
[solutions] |

Jan.15 | Review of expectations, joint distributions, independence. Moment
generating functions and characteristic functions.
Conditional expectation and change of measure.
[lecture notes] |
[problem set 2] - hand in questions 9 and
10.
[solutions][more solutions] |

Jan.22 | Taking limits of random variables, exchanging limits. Stochastic
processes, martingales, Markov chains.
[lecture notes] |
[problem set 3] - hand in questions 8 and
2.6 from the textbook.
[solutions] |

Jan.29 | Stochastic processes in continuous time (martingales, Markov
property). Brownian motion. Approximating Brownian motion.
Generalized Brownian motion as the limit of the binomial model.
[lecture notes] |
[problem set 4] with [BM
part] - hand in questions 7 and 10.
[solutions] |

Feb.6 | Itô integration and Itô's lemma.
[lecture notes] |
[problem set 5] - hand in questions 4 and
5.
[solutions] |

Feb.12 | Proof of Itô's lemma and Itô's lemma for Itô
processes.
[lecture notes] |
[problem set 6] - no assignment this week.
[solutions] |

Feb.19 | READING WEEK | |

Feb.26 | MIDTERM | |

March 5 | Diffusions, SDEs and weak/strong solutions. Financial
applications: derivation of the Black-Scholes-Merton PDE.
[lecture notes] |
[problem set 7] - hand in questions 4.13 and
4.18.
[solutions] |

March 12 | First and second fundamental theorem of finance. CMG formula.
[lecture notes] |
[problem set 8] - no assignment this week.
[solutions] |

March 19 | Risk-neutral pricing. Put-call parity. Martingale
representation theorem.
[lecture notes] |
[problem set 9] - no assignment this
week.
[solutions] |

March 26 | Feynman-Kac.
[lecture notes] |
[problem set 10] - no assignment this week. |

Monday, April 5 | FINAL EXAM |