A course notes on advanced financial models by Michael R. Tehranchi

This course is about models of financial markets, with an emphasis on the pricing and
hedging of contingent claims within such models. Our starting point is the self-evident
observation:

The future is uncertain.

Indeed, anyone with even a passing acquaintance with finance knows that it is impossible
to predict with absolute certainty how the the price of an asset will fluctuate. Therefore,
the proper language to formulate the models that we will study is the language of probability
theory. An attempt is made to keep this course self-contained, but you should be
familiar with the basics of the theory, including knowing the definition and key properties
of the following concepts: random variable, expected value, variance, conditional probability/
expectation, independence, Gaussian (normal) distribution, etc. Familarity with measure
theoretical probability is helpful, though a crashcourse on probability theory is given in an
appendix.

No. of pages : 103

Contents:

1.  One Period Models

2.  Multi Period Models

3.  Brownian Motion and Stochastic Calculus

4.  Black-Scholes Models and Generalization

5.  Interest Rate Models

6.  Crash Course on Probability Theory