Everything you ever wanted to know about what I did, what I published
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I've studied and implemented in C++ affine and quadratic models of diffusion with jumps for option pricing (like cliquet).
I've grounded my work on the article written by D. Duffie, J. Pan and K.J. Singleton : "Transform analysis and asset pricing for affine Jump-Diffusions", (Stanford University, Graduate School of Business - 2000). Indeed, some of their work can be adapted to quadratic models, that's what I had to do.
I've also implemented numerical integration methods for ODE (including Runge-Kutta algorithm with adaptive stepsize and the Bulirsch-Stoer method).
I've calibrated those models on data market to benchmark them in terms of speed of computation and efficiency.
My internship ended with two presentations of my work, one for Barcap's Quant Group and another one at the Ecole Polytechnique. Click here for the abstract of my report.
During the first semester in the MSc in Mathematics in Finance, I was involved in a very interesting project : creating a quant library in C++. Simon LEGER, Aloke MUKHERJEE, Yann RENOUX and I, launched the terreneuve-project.
For this project we used Tortoise CVS to share, update and merge our code.
Our library includes:
- common objects : Date class, interpolator, matrix, random numbers generator
- Black-Scholes and Monte Carlo pricer
- yield curve and credit curve
- assets, portfolio, rainbow option, convertible bonds, variance swaps and exotic products
- IR vanilla swaps, treasury bonds and risky bonds
Our code, report and documentation are available on http://terreneuve.sourceforge.net
As a student at the Ecole Polytechnique, I had to worked on a PSC (wich stands for Projet Scientifique Collectif and means Scientific Team Project) with six other students.
This six-month project on Transmission of Information and Herd Behavior in Finance was supervised by Pr Rama Cont.
The project was divided into three parts :
- the sociological approach, aimed at pointing out the patterns of behavour,
- the computation part, which recquired us to model the transmission of information and the behaviors of traders depending on the information they get; and finally
- applying mathematical tools to a real case, we showed that depending on the way the information is transmitted, it may happens that individual rational behavors leads to irrational results. And that raises the issue of market efficiency
Click here for the report.
I'm the author of an educational memo about Complex Numbers for Atlas Publishers. It's available here.