AMAT
581
(Winter 2006)

"Advanced Futures and Options"

__Course Outline__

*Instructor:*

"Advanced Futures and Options"

W: 12:00pm-13:00; F:10:00am-11:00am

Wednesday |
Friday |

13-14:15
(75 minutes) |
11am-12:15 (75 minutes) |

1)
Stochastic Calculus and the Dynamics of Asset Prices

2) Martingale Theory and Risk-Neutral Valuation

3) Interest Rate Models

4) Energy and Commodity Markets

6) Value-at-Risk and Risk Management

2) Martingale Theory and Risk-Neutral Valuation

3) Interest Rate Models

4) Energy and Commodity Markets

6) Value-at-Risk and Risk Management

First
Class: Wednesday, 11, 2006, 13:00

**Last day of class**: Wed, April 12, 2006.

Winter Session Final Examinations: April 17-28, 2006

*Recommended
texts:*

Lecture Notes

Course Information Sheet

**Course
Web Page**:

The current official syllabus for this course is available in the wall pockets across from MS 476 and

on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate.

There is also a web page for this course which contains the course outline, tentative course schedule, grading scheme, important class dates, etc.

Announcements made in class will be posted there (see end of this web-page). The address of this web page is:*http://www.math.ucalgary.ca/~aswish/amat581W06.html/*

Winter Session Final Examinations: April 17-28, 2006

Lecture Notes

Course Information Sheet

The current official syllabus for this course is available in the wall pockets across from MS 476 and

on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate.

There is also a web page for this course which contains the course outline, tentative course schedule, grading scheme, important class dates, etc.

Announcements made in class will be posted there (see end of this web-page). The address of this web page is:

* Class
work:
In-class lectures with typical examples (lecture notes will be posted
on
the webpage in the form of pdf-files*);

your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).

*Grading
scheme (Course Evaluation):*

Assignments,
Project |
Due
Dates for Assignments and Project |

Assignmnmets:
50% |
A1:Jan
27; A2:Feb 10; A3:Feb 27; A4:Mar 10; A5:Mar 24 (in-class) |

Project:
50 % |
April
12, 2006 (in-class) |

Tentative Lectures Schedule for AMAT 581

Month |
Days |
Wednesday/Friday |

Jan |
11/13 |
Lec1/2:
Course Outline.
Introduction to Options and Futures. Probability Spaces, Sigma
Algebras, Stopping Times. |

Jan |
18/20 |
Lec3/4: Conditional Probabilities and Expectations: Definitions, Basic Properties. Discrete-Time Martingales, Sub- and Supermartingales: Definition and Examples. Martingale Transforms and Representation Theorem. |

Jan |
25/27 |
Lec5/6: Discrete (B,S)-Security Markets: Definitions and Basic Properties. Risk-Neutral Valuation: Cox-Ross-Rubinstein Formula. General (B,S)-Security Markets: Definition, Basic Properties. |

Feb |
1/3 |
Lec7/8: Continuous-Tine Martingales, Sub- and Supermartingales: Definition and Examples. Wiener Process and Poisson Process. Stochastic Integration: Ito Integral. |

Feb |
8/10 |
Lec9/10:
Stochastic Differential
Equations and Ito Formula. Integration by Parts
Formula. Martingale Representation Theorem in Continuous Time (Brownian
Representation) and Levy Characterization of
Brownian Motion. |

Feb |
15/17 |
Lec11/12: Girsanov Theorem. Continuous (B,S)-Security Markets: Definitions and Basic Properties. |

Feb |
22/24 |
Reading
Week (no classes) |

Mar |
1/3 |
Lec13/14: Risk-Neutral Valuation,Black-Scholes Formula, Call-Put Parity, The Greeks. |

Mar |
8/10 |
Lec15/16:
Stopping Times, Wald's Identities, American Options. |

Mar |
15/17 |
Lec17/18:
Interest Rate Models I: Modelling, Yield Curves, Bond Option
Prices. The
Ornstein-Uhlenbeck and Vasicek Models. |

Mar |
22/24 |
Lec19/20:
Interest Rate Models
II:
The
Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models. |

Mar |
29/31 |
Lec21:
Commodity Markets:
Introduction (ppt). Lec22: Energy and Commodity Markets: Definitions and Examples, Modelling, Main Statistical Instruments.I (pdf). |

Apr |
5/7 |
Lec23/24:
Stochastic Modeling of Energy and Commodity Price Processes. |

Apr |
12 |
Lec25:
Value-at-Risk:
Definition and Examples, Basic Calculations. Risk Management. |

Announcements:

5)
Assignment #5: Due-March 24, 2006 (in-class) 4) Assignment #4: Due-March 10, 2006 (in-class) 3) Assignment #3: Due-February 27, 2006 (Drop-Off Box, MS552) 2) Assignment #2: Due-February 10, 2006 (in-class) 1) Assignment #1: Due-January 27, 2006 (in-class) |