DESCRIPTION

The Finite Difference Method (FDM) for Ordinary, Partial and Stochastic Differential Equations

This is a combined course in the sense that is aimed at both beginners (little or no knowledge of FDM) and more advanced students and participants (some working knowledge of FDM):

Modules A–F (Beginners) Fundamentals of FDM, basic support, price Euro 795 excl. VAT

Modules A–H (Advanced) support and help with advanced FDM and optional student project, price Euro 1495 excl. VAT for full-time students and Euro 2495 excl. VAT for those working in industry.

For beginners, having completed modules A to F it is possible to continue with modules G, H and a possible project. If you have any queries please do not hesitate to contact me, Daniel Duffy dduffy@datasim.nl.

 

Click here for course contents.

 

Summary: What does this Course offer?

The main goal of this course is to learn both FDM fundamentals and advanced state-of-the-art FD schemes for one-factor and two-factor option pricing and hedging applications in the finance industry. It should appeal to quant analysts, quant developers as well as MSc/MFE students of Financial Engineering.

The course starts officially March 15 2022. It is possible to register at any time.

Originator and coach: Dr. Daniel J. Duffy, Datasim Education BV.

Daniel Duffy has BA (Mod), MSc and PhD degrees in pure, applied  and numerical mathematics (University of Dublin, Trinity College)  and  he has  been  active in  promoting  partial  differential  equations  (PDE)  and the Finite  Difference  Method  (FDM)  for  applications  in computational  finance.  He  was  responsible  for  the introduction  of  the  Fractional  Step  (Soviet  Splitting) method  and  the  Alternating  Direction  Explicit  (ADE) method in computational finance. He is also the originator of the exponential fitting method for time-dependent partial differential equations.

Daniel Duffy has extensive experience in coaching, training and project supervision in both industry and academia. He has successfully supervised more than forty MSc/MFE projects in computational finance using C++ to implement PDE/FDM models.

Background

A differential equation (DE) is an equation involving an unknown function of several independent variables and derivatives of this function. The DE is defined in continuous space-time and we normally need to define auxiliary conditions to ensure that the solution of the DE exists and is unique. In general, it is not possible (nor practical) to compute an analytical or quasi-analytic solution of a DE and for this reason we must resort to numerical methods, of which there are many. In this course we concentrate on the Finite Difference Method (FDM) because it is relatively easy to understand and to implement. It is by far the most popular method for a range of problems in mathematics, engineering and computational finance.

What is this Online Course?

The goal of this in-depth and hands-on course is to learn the mathematical foundations of the Finite Difference Method (FDM) and to use it to approximate the solution of a range of differential equations that occur in areas such as mathematics, engineering and computational finance. In general, it is difficult to find analytical solutions to differential equations and for this reason we choose a suitable finite difference scheme that computes an approximate solution that is accurate, is easy to implement and that has good performance (we quantify these terms in the course).

Traditionally, the Finite Difference Method (FDM) is a subject that is taught in numerical analysis courses and it finds many applications in engineering and more recently, finance. The most famous (but not the only) scheme is the Crank Nicolson (CN) method for the Black Scholes equation and CN has been used as a one size fits all recipe to solve PDE problems in finance. For more complex problems, the method can break down and more robust and predictable schemes have been established in the Datasim courses. It is for these reasons that we have originated this course for students and working professionals with background in, for example economics, computer/data science and financial mathematics. In short, this course assumes no prior knowledge of FDM.

What do you receive?

This depends on whether you opt for Course A-F (Beginners) or Course A-H (Advanced). In the latter case we provide support and the possibility (if the student wishes) to do a PDE/FDM project. We strongly recommend your doing the Course A-H if you are interested in extra support and coaching.

• Lifelong access to the videos; hardcopy of course sent to your home address (please be sure that the packet will be accepted at that address!).
• The e-book version of NUMERICAL METHODS IN COMPUTATIONAL FINANCE, A Partial Differential Equation (PDE/FDM) Approach by Daniel J. Duffy.
• Source code that implements PDE and ODE models (where applicable). The follow-on courses from Datasim are concerned with the numerical approximation of PDEs by the Finite Difference Method (FDM).
• Students send solutions to exercises using LATEX, ideally (LATEX is easy to learn). (Advanced only).
• A signed certificate on successful completion of the course. (Advanced only).
• An initial Skype meeting to set up the course plan and a final Skype meeting prior to certification. (Advanced only).

For whom is this Course?

This course has been developed for anyone who wishes to learn what the finite difference method is and how to apply it to real-life applications. No previous knowledge of PDE/FDM is required. Some knowledge of calculus and linear algebra is assumed and we also review these topics in  the course as essential refresher videos. In this sense the course is reasonably self-contained.

The three main target groups for the course are:

• MSc and MFE students who need to be familiar with FDM techniques as entrance requirement to university degrees in finance. It puts you in the enviable position of being able to price various forms of the Black-Scholes equation using several modern state-of-the-art finite difference schemes.
• Industry quants who may not have had exposure to PDE/FDM techniques (for example,  those quants with a stochastics background) but who wish to complement existing knowledge of Monte Carlo and stochastic simulation techniques.
• Experienced quants who have practical pricing and hedging experience and who wish to gain a deeper mathematical and numerical understanding of PDE/FDM techniques and to apply them to price and hedge a range of one-factor and two-factor equity and fixed income models.

Some Testimonials

“FDM is one of the most useful and advanced courses that I have ever taken.  The tools that I learnt were directly applied to value complex derivatives contracts, in an efficient manner using C++, such as convertible bonds and Bermudan callable bonds.  On the other hand, Daniel is an extraordinary tutor who helped me out in every step of the final applied project.”

- Jaime Maihuire Irigoyen - Sustainable Investing Research Associate, BlackRock, Inc.

"Professor Duffy’s course provides a comprehensive look at the Finite Difference Method in financial applications. He was readily accessible and provided a great balance of clear direction with room for independent research."

- Thomas M. - TDM Trading.

"Actually I've searched a few PDE online courses, most of them are not closely connected to computational finance, while the Datasim course is designed for it and very well structured."

- Prospective MFE student

 

We give a student discount. The student price is Euro 1500 (no VAT if you are outside EU). The courses remain accessible forever and you can plan your own schedule but in general it should be possible to complete a course (including exercises and mini-project) in 2-4 months.  See also our Frequently Asked Questions (FAQ) on the Datasim site. Please contact dduffy@datasim.nl