Introduction to Asset Pricing

Professor: Aimé Scannavino, Panthéon-Assas University

Objective: The aim of the course is to introduce the basic asset pricing theories: CAPM and related models, models for swaps, forward / futures and options. A particular attention is dedicated to options: the Black-Scholes model is carefully set out (after a presentation of stochastic calculus basis: Ito processes and Ito lemma); the course outlines as clearly as possible its link with Cox-Ross-Rubinstein's analysis and Arrow-Debreu's General Equilibrium with Contingent Claims. Financial strategies through stochastic simulations are also exposed.

Outline:

Part 1:

1. Utility functions with risk aversion
2. Efficient frontier
3. The concept of "market portfolio"
4. The CAPM
5. Passive portfolio management and beta valuations
6. Active management beyond the MEDAF: bonds and swaps

Part 2:

1. Forward markets and future markets
2. ITP and their conditions of validity
3. Determination of a futures price according to information contexts
4. Futures arbitrage trades
5. Instruments and strategies
6. General Equilibrium theory with Contingent Claims applied to securities valuations
7. The binomial model of Cox-Ross-Rubinstein (discrete time) for the evaluation of European-style options

Part 3:

1. Brownian Motion and Geometric Brownian Motion; Ito's formula; considerations on the stochastic integral; the Black-Scholes model for the evaluation of European-style options (continuous time); proof of the Black-Scholes formula; implementations of the formula
2. Black-Scholes limitations: volatility issues; non-Gaussian stock prices; stock prices with non-continuous trajectories…