AMAT
581/681
(Fall
2015)

"Stochastic Calculus for Finance"

__Course Outline__

*Instructor:*

"Stochastic Calculus for Finance"

TuTh:11:00am-12:00pm

Tuesday |
Thursday |

9:30am-10:45am (75 minutes) |
9:30am-10:45am (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

7) Levy Processes in Finance

2) Martingale Theory and Risk-Neutral Valuation

3) Interest Rate Models

4) Energy and Commodity Markets

6) Value-at-Risk and Risk Management

7) Levy Processes in Finance

First Class:
Tuesday, September 8, 2015, 9:30am

**Last day of class**: Tue, December 8, 2015

**A#1-5 due dates**: Sep22, Oct6, Oct20, Nov3, Nov17

**Project due date**: Dec 8, 2015

*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/amat581_681Fall2015.html/*

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:Sept22; A2:Oct6; A3:Oct20; A4:Nov3; A5:Nov17 |

Project: 50 % |
Dec 8, 2015 ()pdf-file sent by e-mail |

Tentative Lectures Schedule for AMAT 581/681

Month |
Days |
Tuesday/Thursday |

Sept |
8/10 |
Lec1/2: Course Outline. Introduction to
Options and Futures. Probability Spaces, Sigma Algebras,
Stopping Times. |

Sept |
15/17 |
Lec3/4: Conditional Probabilities and Expectations: Definitions, Basic Properties. Discrete-Time Martingales, Sub- and Supermartingales: Definition and Examples. Martingale Transforms and Representation Theorem. |

Sept |
22/24 |
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. |

Sept/Oct |
29/1 |
Lec7/8: Continuous-Time Martingales, Sub- and Supermartingales: Definition and Examples. Wiener Process and Poisson Process. Stochastic Integration: Ito Integral. |

Oct |
6/8 |
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. |

Oct |
13/15 |
Lec11/12: Girsanov Theorem. Continuous (B,S)-Security Markets: Definitions and Basic Properties. |

Oct |
20/22 |
Lec13/14: Risk-Neutral Valuation, Black-Scholes Formula, Call-Put Parity, The Greeks. |

Oct |
27/29 |
Lec15/16: Stopping Times, Wald's Identities, American Options. |

Nov |
3/5 |
Lec17/18: Interest Rate Models I: Modelling, Yield Curves, Bond Option Prices. The Ornstein-Uhlenbeck and Vasicek Models. |

Nov |
11-15 |
Reading Days (no
classes) |

Nov |
10/17 |
Lec19/20: Interest Rate Models II: The Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models. |

Nov |
19/24 |
Lec21/22: Energy and
Commodity Markets: Definitions and Examples,
Modelling, Main Statistical Instruments I (pdf). (Geman Book: Intro) |

Nov/Dec |
26/1 |
Lec23/24:
Stochastic Modeling of Energy and Commodity Price
Processes. (Geman Book: Chapter 3) Change of Time Method in Finance Quantitative, Energy and Environmental Finance |

Dec |
3/8 |
Lec25/26: Value at Risk and Risk
Management. Levy Processes in Finance. |

Announcements:

Assignments5) Assignment #5:
Due-November 17, 2015 (in-class)
4) Assignment #4: Due-November 3, 2015 (in-class) 3) Assignment #3: Due-October 20, 2015 (in-class) 2) Assignment #2: Due-October 6, 2015 (in class) 1) Assignment #1: Due-September 22, 2015 (in-class) Projects
(pdf-file sent by e-mail):
Due-Tuesday, December 8, 2015 |