Simon Leger at NYU
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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.

My 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.

Title : Monte Carlo pour les nuls
Abstract :  Le but de ce papier est de donner une introduction aux techniques 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 efficacite.
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.

Title : Monte Carlo for the noobs
Abstract : The purpose of this paper is tointroduce Monte Carlo techniques used in finance, mainly to price complicated products, called exotics. 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.

Title : Summer internship research
Abstract : 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.

Title : 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 options...


My projects :

  • Small Quantlib interface
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 website : http://terreneuve.sourceforge.net/

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.

  • Pricing of CDO with Gaussian Copula
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.


  • Simulation of realistic daily stock prices
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.

  • CSplash
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 :
Handout for the trading game
Second hour : binomial tree exemple, and more...
The results of the trading game can be downloaded here : results of the game

  • Cost of hedging for options, pure dynamic and two-sided hedge
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 costs 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%.
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 simulations again.
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...

  • Model validation for Rainbow options
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 : HwRiskModelValidation.pdf