Mat-2.194 Summer School on Systems Sciences

Financial Engineering


Assistant Professor Jussi Keppo from Michigan University


Teaching Assistant

Erkka Näsäkkälä



The main objectives of the course:

We begin by exploring the implications of the absence of static arbitrage. We study, for instance, forward and futures contracts. We proceed to develop the implications of no arbitrage in dynamic trading models: the binomial and Black-Scholes models. The theory is applied to hedging and risk management.

Preliminary knowledge

The students should be familiar with the fundamentals of probability theory and investment analysis.


Exam 60%, homework 40%.

Grades of the course

Course Material

Hull, J.C.: Options, Futures, and Other Derivative Securities, 1999, Prentice-Hall.

Homework Problems

During the help sessions the students will solve problems under the guidance of Teaching Assistant. The students will be given homework problems after each help session. The homework problems must be handed in before the start of next lecture. The homework problems must be solved independently and they will be graded.

Homework 1

Homework 2

Homework 3

Preliminary Schedule

All the lectures will be held in the classroom Y427B

Lecture 1 28.5 14-16

  • Introduction to derivative securities; pricing of forward and futures.

  • cost of carry model

  • hedging of forwards and futures

  • the difference between forwards and futures

    Help Session 28.5 16-18

  • Interest rate futures; forwards and futures examples.

    Lecture 2(HW1 Due) 29.5 14-17

  • Basic no arbitrage restrictions for options
  • elementary option strategies.

  • upper and lower boundaries for American and European options

  • put-call parity

  • definition of option strategies and their payoffs

    Lecture 3 30.5 14-16

  • Binomial option pricing.

  • binomial model for underlying asset

  • hedging of options

  • risk-neutral pricing

  • pricing of American options

    Help Session 2 30.5 16-18

  • Examples on options

    Lecture 4 (HW2 Due) 31.5 14-16

  • The Black-Scholes analysis.

  • continuous-time stochastic model

  • hedging options in continuous-time

  • Black-Scholes differential equation

    Help Session 3 31.5 16-18

  • Examples on continuous-time option pricing

    Lecture 5 (HW3 DUE) 1.6 14-16

  • General derivative pricing approach; risk management with options

  • pricing with nontradable underlying asset

  • partial derivatives of options

  • general risk management approach

    Take home Exam

    Load your exam here

    Exam will be available here 3.6.2001 at 18.00. Exam will also be emailed to course participants.

    Exam must be handed in 4.6.2001 at 18.00 eihter by email or by returning a paper version to a paper bag at Systems Analysis Laboratory (near by U241)