46-944: Stochastic Calculus for Finance 1

Spring 2017

Course Description

The first half of this course introduces martingales, Brownian motion, Itô integrals and Itô’s formula, in both the uni-variate and multi-variate case. This is done within the context of the Black-Scholes option pricing model and includes a detailed examination of this model. The second half of the introduces exponential martingales and the Girsanov theorem. This is done in the context of risk neutral measures and the fundamental theorems of asset pricing.

Prerequisites

• 46-921: Introduction to Probability
• 46-941: Multi-Period Asset Pricing

Text Book

• Stochastic Calculus for Finance II by Steven Shreve. (We will cover roughly the first five chapters.)

Class Policies

Lectures

• If you must sleep, don’t snore!
• Be courteous when you use mobile devices.

Homework

• Homework is due at the beginning of class on the due date.
• Late homework policy: Homework turned in within 48 hours of the deadline will be accepted.
  • Late homework turned in within the first 24 hours of the deadline will receive a 10% penalty. In particular, homework turned in even one nanosecond after class starts, will receive this penalty.
  • Late homework turned in within the next 24 hours will receive a 25% penalty.
  • Homework more than 48 hours late will not be accepted.
  • To account for unusual circumstances, your lowest homework will not count towards your grade.
  • I will only consider making exceptions to the late homework policy for severe and extreme emergencies that require your absence for more than 12 days.
• Solutions will usually be posted 48 hours after the homework deadline. Due to holidays or exams solutions to some assignments might post earlier. In this case, you will be notified of this in advance, and late homework will not be accepted after solutions have been posted.
• You can choose how you want to turn in your homework: Physically to me, in class, or by scanning it and uploading it on blackboard. Please ensure your scans are a high quality PDF, as photos of your homework will not be accepted. You may not turn in homework by putting it in one of our mailboxes or under our doors.
• You may collaborate on the homework, however, you may only turn in solutions which you fully understand and have written up independently. Violation of this policy will be treated seriously according to procedures in the MSCF student handbook.

Exams

• No notes, calculators, computational aids, or internet enabled devices are allowed during exams.
• You may not give or receive assistance during exams.
• Violation of these policies will be treated seriously according to procedures in the MSCF student handbook.
• If you earn a C+ or lower, and have at least a 70% average on the homework, you may take the makeup final. Your performance on the makeup final can not reduce your grade, and can only increase your grade in the course by at most a full letter, up to a maximum of B–.

Grading

• Your performance on the homework, midterm and final will each be converted to a numerical grade 0 and 4.5 “using a curve”.
• Your overall grade will be computed as a weighted average with the final counting for 50%, midterm 30% and homework 20%, with homework grade capped by the exam average.
  • Explicitly, your exam average E is computed using E = (5F + 3M) / 8, where F and M are your final and midterm grades respectively.
  • Now your overall grade A given by A = .8E + .2 min(H, E), where H is your homework grade.
• Your final letter grade will be computed from your numerical grade using the standard scale.