84219 - Computational Finance

Learning outcomes

The objective of the course is to address frontier topics in computational finance. At the end of the course the student will muster the skill needed to select the most appropriate model for the problem at hand, set up a numerical simulation with the most appropriate methodology, judge the quality of the results from data analysis, and he/she will have enough knowledge to set up benchmark to test for the accuracy of the numerical results. The topics addressed will refer to state-of-the-art issues in pricing, risk management and numerical techniques.

Course contents

The course aims to present the main computational tools used in the field of derivative pricing and risk management with a particular focus on the problem of early exercise.

1. Option Payout and Early Exercise
1. American and Bermudan Options
2. The optimal stopping time problem
3. Difficulties in the valuation of American Options

1. Trees for Option Pricing
1. Binomial Trees
2. American Options on trees: rolling-back on the tree

1. Numerical Solution of Partial Differential Equations
1. Linear System
2. Finite Difference Methods

1. Monte Carlo Methods
1. Introduction
2. Quasi-Montecarlo
3. Longstaff-Schwartz Method
4. The Brownian Bridge Method

Office hours

See the website of Giovanni Della Lunga