Library:
Madrid
London
Paris Champerret
Paris Montparnasse
Turin
Monte Carlo methods are often used in the valuation of financial derivatives. Based on Monte Carlo simulation, time discretizing methods are developed to simulate when no exact solution exists. However, those methods can only be regarded as a biased estimation. In 2015, an unbiased estimator for Monte Carlo simulation is developed by Rhee and Glynn. The aim of this research is to study and implement these techniques (using Python for all the simulations).
In this thesis we will first lay the background of this paper out, including the concept of financial options and the often used pricing theory, which leads to the well-known Black-Scholes model. After that, two Monte Carlo approximation methods will be studied: the Euler-Maruyama method and the Milstein method. We will then compare the results to the exact Black-Scholes model, before analyzing the convergence order of the two implemented methods. To conclude, we will then implement the unbiased simulator based on Milstein scheme and compare the results with the exact Black-Scholes model.
