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Probability and Finance I


Cassese G.

Course director


The course gives an elementary introduction to probability theory and stochastic processes for finance, by focusing on discrete probability spaces. Starting with a simple binomial market model, the key concepts of probability and of financial modeling are introduced simultaneously. These are then extended to the framework of a multiperiod model. Concerning probability, we introduce and define the notions of random variable, conditional and unconditional expectation, stochastic processes, martingales and Markov processes. Concerning financial applications, we discuss topics such as arbitrage, replication, hedging, derivative pricing and optimal portfolio selection. All definitions are supported by simple numerical examples and exercises that guide students through the program.

There will be a written exam in the form of numerical problems.

Table of contents

  1. The Binomial no-arbitrage pricing model
    1. Binomial model;
    2. Arbitrage free-pricing;
    3. Computational aspects.
  2. Discrete probability theory
    1. Probability space;
    2. Random variables;
    3. Expectation and conditional expectation;
    4. Martingales.
  3. State prices and measure change
    1. Risk-neutral measure and changes of measure;
    2. Densities and Rado-Nikodym derivatives;
    3. Capital asset Pricing Model;
    4. Bond pricing and forward neutral measure.

Reading material
Shreve, S. (2004), Stochastic Calculus in Finance, Vol. 1, Springer-Verlag, New York.

Karr, A., F., K. (1993), Probability, Springer Verlag, New York.