318201 Probabilistic Methods in Finance (V) (SoSe 2008)

From the QEM intranet:

• General Presentation :*

The main objective of this course is to provide a theoretical framework
for the pricing of derivative securities, which are securities whose
values depend on the values of other financial assets (underlying
assets), like futures and options.

We begin with a description of the derivative products and their use.
The second part shows how the assumption of no arbitrage enables forward
prices to be obtained from underlyer's price. Different examples are
considered (equities, commodities, currencies, interest rates...). The
third part explains why a model of the process of underlyer's price is
necessary to price an option. Option pricing is then studied in
discrete-time (model of Cox-Ross-Rubinstein), which allows us to expose
main concepts of risk-neutral valuation and hedging, useful in
continuous-time too. After an elementary introduction to necessary
mathematical tools (Brownian motion, stochastic processes and Itô's
lemma), we develop lastly the classical continuous-time Black-Scholes model.

Requirements for participation, required level

Probability Theory (Part 1)

Bibliography

• Book:* HULL John, 2005, Options, Futures, and Other Derivatives, 6th

edition, Financial Times