On Percolation Theory for Agent-Based Financial Modeling
We apply percolation theory to financial modeling through the Cont-Bouchaud model. The project deals with the complete implementation in Java and testing of this model. We also derive major results and completely describe the statistics of the model. A significative part treats the implementation of an algorithm able to efficiently find clusters in a lattice. We then present some results from percolation theory, and then discuss and implement the Cont-Bouchaud model. The results we find from percolation theory are in accordance with the literature. We find that the Cont-Bouchaud model is capable of generating results distributed as both a Gaussian and a power law, in function of the activity probability. The exponents found for the power law are also in accordance with the literature. A final part is dedicated to presenting and discussing the implementation of the model in Java.
Submitted and defended on September 9, 2009 as part requirement for the MSc Degree in Computer Science at University College London
On Numerical Methods for the Pricing of Commodity Spread Options
We study numerical methods to price commodity spread options. We first present spread options and particularly the crack spread options paying the buyer the difference between the crude oil and heating oil futures prices. We then present the Monte Carlo option pricing pricing framework and discuss its application to spread option pricing. Finally, we discuss some variance reduction techniques and show their efficacy in front of a classic Monte Carlo computation.
Submitted on September 11, 2009 as part requirement for the MSc Degree in Financial Engineering at Birkbeck College
On Lévy Processes for Option Pricing: Numerical Methods and Calibration to Index Options
Since Black and Scholes published their article on option pricing in 1973, there has been an explosion of theoretical and empirical work on the subject. However, over the last thirty years, a vast number of pricing models have been proposed as an alternative to the classic Black-Scholes approach, whose assumption of lognormal stock diffusion with constant volatility is considered always more flawed. Relaxing the assumption of continuous sample paths, leads to jump models, where stock prices follow an exponential Lévy process of jump-diffusion type (where evolution of prices is given by a diffusion process, punctuated by jumps at random intervals) or pure jumps type. This thesis deals with the study of Lévy processes for option pricing, reviewing first the theory and literature and eventually proposing elegant numerical methods in order to price index options and calibrate the models' parameters on real option data.
Submitted and defended on April 28, 2008 as part requirement for obtaining the title of Dottore Magistrale in Finance at Università Politecnica delle Marche