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
Shreve, S. (2004), Stochastic Calculus in Finance, Vol. 1, Springer-Verlag, New York.
Karr, A., F., K. (1993), Probability, Springer Verlag, New York.