10h30 - 10h55
Dynamic programming for valuing American options under variance-gamma process
Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of pure-jump Lévy processes such the variance-gamma model. In this setting, explicit solutions for derivative prices are unavailable, for instance for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing American-style options under an extended variance-gamma model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on the S&P 500 futures contracts.
10h55 - 11h20
A QR-Factorization-Based Algorithm for Constrained Least-Squares Problems
We present an interior-point method for linear least-squares problems with both equality and inequality constraints. The algorithm is based on a QR factorization of the least-squares operator rather than a symmetric indefinite factorization of the KKT matrix to improve numerical stability. We show several formulations of the KKT system and their solution using QR factorization. Numerical results demonstrate the effectiveness of the method.
11h20 - 11h45
Kernel Mean Matching for Causal Inference
Computing a causal effect from observational data needs to be done carefully in order to obtain an unbiased estimate. In this talk, we give a short introduction to causal inference and to the existing approaches that accomplish this task. We then show how to adapt kernel mean matching, an approach designed for the covariate shift problem in machine learning, in order to compute a causal effect from observational data. We also show how to improve the tuning phase of this approach. We finish by comparing this approach to the state-of-the-art using data from a realistic generative model.