Welcome to my web page
I am currently student in the MSc of Financial Mathematics at
NYU. I am French, 24 and decided to come here after being at the ENSAE
in Paris. I live in Soho where I can enjoy the great pubs and
restaurants, without being too far from NYU !
I am willing to become a quantitative trader, a field in
which I have some experience as you can see on my resume, and I
recently started writing some financial articles.
So, I just recently started writing some articles, the first one being
on Monte Carlo. I wrote also a small paper to explain the
recruitment process for summer internships and my latest paper is going
to be on the known closed formulas for option prices and their proofs.
You can download them by clicking on the titles.
: Monte Carlo pour les nuls
Le but de ce papier est de donner une introduction aux
de Monte Carlo utilisees en finance, essentiellement afin de pricer des
produits assez complexes, dits exotiques. Ce papier
s'adresse a un
publique non experimente et se veut d'approche assez generale bien
qu'expliquant comment construire efficacement un tel produit en
informatique et en donnant les m\'ethodes permettant d'ameliorer son
En partant de l'origine du principe de Monte-Carlo, nous verrons
comment ceci nous permet de pricer des produits financiers, puis
comment implementer un tel systeme. Enfin nous aborderons certaines
techniques permettant d'en ameliorer l'efficacite.
: Monte Carlo for the noobs
Abstract : The
purpose of this paper is tointroduce Monte Carlo
techniques used in finance, mainly to price complicated products,
This paper has been designed for a non-expert public and focuses on
giving a broad overview of Monte Carlo techniques from a practical
point of view and presents also some improvements that can be done to
increase the efficiency.
After explaining where this technique comes from, we will see how we
can price financial products with it and how to implement such a
system. We will also get an overview of more complicated techniques
that allow us to improve its efficiency.
: Summer internship research
The purpose of this paper is to give some advices to those who are
looking for an internship. We will discuss both summer internship
recruitment process and longer term internships.
: Known Closed Formulas and their
proofs (in progress...)
Abstract : In
this paper, we will try to give every known closed formula for options
and also their proof(s). We are going to work under the Black Scholes
equation for the diffusion of the process.We will start with a
classical call option, try to give a few proofs of its price and then
move on to more complex products, such as barrier options, quanto
For the first semester of the master, we had to set up a big project,
with a team of four people,. We built a light Quant Lib interface,
using CVS to merge our files which allowed us to work on the project
remotely at the same time.
Our project under sourceforge can be downloaded via this page : http://sourceforge.net/projects/terreneuve
and more informations can be found under this
As you can see there, you can download the whole code, with the project
files for use with Visual Studio.NET, the final report in pdf format
(and source in tex) and also a Doxygen documentation.
This was one homework for the Credit modelling class, weh ad to model
tranches of CDO with gaussian copulas by MC simulation, simulating
default times and pricing CDOs. This project has been done in VBA with
a nice Excel interface, you can download the file here with
the VBA code accessible : CDOPricingProject.xls.
- Pricing of CDO with Gaussian
Here is a C++ project in which you can specify (in the main
function) a number of stocks, number of days and the weights you want
to give to two market factors which will drive your market and the
results will be outputed in a text file which you can easily copy/paste
to any other program since it is comma separated values. I assumed
lognormal distribution for stock volatilities whose mean and standard
deviation can be specified. The zip code can be downloaded here : StockGenerator.zip.
- Simulation of realistic daily stock prices
This was a one day teaching class at Courant Institute, NYU for high
school students, Yann and I taught a class, an introduction to
financial mathematics, here are the documents of our class, the
description can be found on the csplash website : http://www.cims.nyu.edu/~csplash/csplashday.php
Here are the course documents :
the trading game
binomial tree exemple, and more...
The results of the trading game can be downloaded here : results of the game
This was a homework for the risk management class. We had to estimate
the P&L and his standard deviation as well as the transaction
for different strategies. We always assume we are short a call and long
the replication portfolio. This portfolio can be either a pure dynamic
replication portfolio, with either 100 or 500 rehedging over the life
time of our option (1 year) or a two-sided hedge + dynamic, meaning we
are also long two half calls with strike around the first one +/-5%.
- Cost of hedging for options,
pure dynamic and two-sided hedge
We calculate all these values for two different kinds of dynamic for
the stock : pure black scholes or also with a volatility on the
volatility : we assume a lognormal diffusion process for the volatility
with a standard deviation of 33%.
Then we also allow jumps on our path : the jumps occur on average once
a path and can be either down or up jumps and we run all these
After this, we consider different types of rehedging, meaning instead
of getting a zero delta, we only rehedge when our absolute delta is
above a certain value and we run these simulations for different
values. All results can be seen on the following spreadsheet : HwRiskSimulationCosts.xls
. I am sorry for the poor quality of the code, but it has been done at
a moment I had a lot of things to do...
This was another homework for the same risk management course where we
had to validate a model. We chose to validate rainbow options since it
was part of our C++ project. We test our prices by different MC
simulations and compare them with the known closed forms values. We
also test it against real historical simulation, by retrieving some
stocks data, implied volatilities at different maturities, risk free
rates and do historical simulation of pricing without rehedging to
compare the prices with the discounted payoff and conclude that our
model can be applied to the pricing of options. The pdf file of our
results can be seen here :
- Model validation for Rainbow