Probability and Finance I

The course gives an elementary introduction to probability theory and stochastic processes for nance, by focusing on discrete probability spaces and their modeling applications. The lecture starts from the setting of a simple binomial pricing model to introduce key probability concepts that are useful for applications. Its covers the concepts of random variables, stochastic independence, conditional and unconditional expectations, and martingale processes, with some examples of applications to the pricing of derivatives in arbitrage-free markets. Finally, the idea of a state price and the relation to measure changes is explained, together with some pricing examples in the context of a Capital Asset Pricing Model.

Grading
There will be a open book, written exam.

Table of contents:

1. The Binomial no-arbitrage pricing model
   (a) Binomial model
   (b) Arbitrage free-pricing
   (c) Computational aspects
2. Discrete probability theory
   (a) Probability space
   (b) Random variables and expectations
   (c) Conditional expectations
   (d) Martingales
3. State prices and measure change
   (a) Change of measure
   (b)Densities and Rado derivatives
   (c) Capital asset Pricing Model
   (d) 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.