Stochastic Calculus

Professor: Céline Chevalier, Panthéon-Assas University.

Objectives: The aim of the course is to present the main applications of stochastic calculus in finance. The approach is directly inspired by John Hull's book Options, futures and other derivative assets. .

Outline:

1. Theory of non-arbitration

• (13) Introduction to Binomial Trees, Discrete Time Modeling
• (14) Modeling in continuous time, Process of evolution of the course of an action, Ito's lemma
• (15) The model of Black and Scholes

2. Calculating the price of an option with Excel

• (19) The Greek letters
• (20) Volatility curves
• (21) The evaluation of options by binomial trees, The evaluation of American options
• (22) The Value-at-Risk.

(The numbers correspond to the chapters of Hull's book)

Grading: Mid-term exam and a final exam at the end of the semester.

Bibliography:

• Hull, 9 édition, Pearson, 2014