Monte Carlo Methods with Applications to Finance


Université catholique de Louvain - Louvain School of Management

Start Date:

End Date:

Application Deadline:

Expired help

Type

Summer schools

Location

Belgium

Start Date:

End Date:

Location

Belgium

Type

Summer schools

Application Deadline:

Expired help


PhD course on "Monte Carlo Methods with Applications to Finance "

By Prof. Gilles Pagès

Laboratoire de Probabilités et Modèles Aléatoires

Université Pierre et Marie Curie Paris VI

March 8-9, 2017

Tuesday 9:00-17:00, Wednesday 9:00-17:00, at ISBA, room C035, voie du Roman Pays 20, 1348 Louvain-La Neuve

Abstract

Monte Carlo Methods are powerful techniques allowing one to numerically estimate any integral with an arbitrarily large degree of precision. In particular, it is often used to estimate probabilities and expectations when, as often the case, no closed form can be easily found. This technique became central in finance in light of the risk-neutral valuation principle resulting from the assumption of no arbitrage opportunities. In this course, we will briefly review the standard Monte Carlo machinery before moving to advanced Monte Carlo schemes, from variance technique reductions to multilevel schemes applied to multivariate stochastic differential equations.

DAY 1 (Unbiased simulation)

  • Basic simulation
    • introduction to convergence and error notions
    • Central Limit Theorem, Law of the Iterated Logarithm
  • Variance reduction techniques
    • control variate
    • antithetic sampling
    • stratification
    • importance sampling
  • Quasi Monte Carlo : from Halton to Sobol sequence of random numbers

DAY 2 (Biased simulation)

  • Univariate discretization schemes for diffusions
    • Euler and Misltein (explicit)  schemes
    • Implicit variants with application to Cox-Ingersoll-Ross process
  • Multivariate schemes & challenges
    • Lévy area
    • From Milstein to antithetic Milstein
  • High  performances bias killing methods
    • Regular and weighted multistep
    • Multilevel simulation
  • Application to nested Monte Carlo Methods

Registration is mandatory

Please send an e-mail to nadja.peiffer@uclouvain.be

  • Members of the organizing doctoral schools : free
  • Academics & PhD students : 100 eur
  • Other : 400 eur

Registration includes access to course, course material, coffee breaks and lunches