94422 - Applied Computational Finance

Learning outcomes

Basic knowledge of the Python and R programming language is assumed. At the end of the course, the student should be able to develop calculation procedures for the pricing of equity with a particular focus on the early exercise problem. 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. Option Payout and Early Exercise American and Bermudan Options The optimal stopping time problem Difficulties in the valuation of American Options Trees for Option Pricing Binomial Trees American Options on trees: rolling-back on the tree Numerical Solution of Partial Differential Equations Linear System Finite Difference Methods Monte Carlo Methods Introduction Quasi-Montecarlo Longstaff-Schwartz Method The Brownian Bridge Method

Course contents

• • The problem of early exercise in derivative pricing
  • Finite Difference Methods for the Numerical Solution of Partial Differential Equations
  • Some Example of Finite Difference Methods: Heston Model, Parisian Option
  • How use Finite Difference Methods for American Option Pricing
  • The curse of dimensionality and the Monte Carlo Approach
  • Least Square Montecarlo
  • Finding the Optimal Exercise
  • Pricing a simple put plain vanilla
    

   

 

Readings/Bibliography

Pietro Rossi, "Lecture Notes on Computational Finance"

Paul Wilmott, "Derivatives, The Theory and Practice of Financial Engineering", University Edition

Paul Wilmott, Sam Howison and Jeff Dewinne, "The Mathematics of Financial Derivatives, A Student Introduction", Cambridge University Press

John C. Hull, "Option, Futures and Other Derivatives", 6th Edition, Prentice Hall

Paul Glassermann, "Monte Carlo Methods in Financial Engineering", Springer

Yves Hilpisch, "Derivatives Analytics with Python", Wiley Finance

Don L. McLeish, "Monte Carlo Simulation and Finance, Wiley Finance

Teaching methods

Lectures (15 h)

Assessment methods

The final exam consists in the development of a python procedure for the pricing of an American-type option. The procedure must be described in a document that will be discussed with me at the time of the exam.

Teaching tools

Lecture Presentation, Jupyter Notebook and code snapshot

Office hours

See the website of Giovanni Della Lunga