Doctorat en administration (Ph. D.) – ingénierie financière

1. Brief review of contingent claims and of the notion of market (in)completeness. The hypotheses underlying to the Black-Merton-Scholes model and the associated pricing kernel. 2. The volatility smile model-free volatility measures (RV and VIX) and option-implied distributions. We will revisit the Black-Scholes implied volatility smile and some of its potential explanations. We will then consider different model-free volatility measures and see how variance swaps and/or option data can be used to extract information about the risk-adjusted distribution of returns. Finally we will introduce the notion of variance risk premia a concept that we will further revisit when we study dynamic volatility models.

Selected papers: Andersen Bollerslev Christoffersen and Diebold (2006); The CBOE Volatility Index - VIX (2009); Demeterfi Derman Kamal and Zou (1999); Martin (2013); Bollerslev and Todorov (2011) . 3.Stochastic volatility models and the pricing kernel. Conditionally normal GARCH models and the pricing kernel in discrete time. Component models.

We will introduce stochastic volatility and GARCH models highlighting the pricing kernel used or implied by the different models. We will review some stylized facts on volatility and see how the different models accommodate these (or not). In particular we will discuss volatility models in which volatility process is separat

- Corporate investments: Real options strategic exercise of real options (option games) liquidity constraints.

- Capital structure: Static trade-off agency conflicts informational asymmetry dynamic capital structure interactions with investment policy.

- Financial distress: Debt renegotiations strategic debt service bankruptcy procedure.

- Corporate control: Mergers and acquisitions industry competition.

- Corporate risk management: Risk management and firm value liquidity constraints.

- Empirical implementation: Estimation of structural models convexity bias and other issues in testing capital structure models.

Monte Carlo simulation

Solution of partial differential equations

Fourier Transform

Filtering and estimation of latent variables

Artificial intelligence

Risk measures

1) Why is there a recent surge of interest in robust optimization?

2) Robust counterpart of Linear Programs

3) Data-driven Uncertainty Set Design

4) Robust Nonlinear Programming

5) Adjustable Robust Linear Programming

6) Value of Flexibility Using Tractable Decision Rules

7) Globalized Robust Counterparts

8) Distributionally Robust Optimization

9) Robust Markov Decision Processes

10) Robust Preference Optimization

11) Pareto Robust Optimization

12) A Survey of Recent Applications