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ODE/PDE/SDE online courses for computational finance

Daniel Duffy

C++ author, trainer
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Online ODE PDE Course

Ordinary and Partial Differential Equations with Applications to Computational Finance

Dr. Daniel J. Duffy (Datasim Education BV) dduffy@datasim.nl

May 2023



Ordinary and partial differential equations (ODE/PDE) have major applications in many areas of science, engineering and computational finance and other important application areas. It is a huge area and it is difficult to know where to start if you wish to learn this subject matter. To this end, this focused, hands-on online course introduces the most important concepts, models and methods to get you up to speed as soon as possible.

Our (unique) approach is to examine differential equations (DEs) from several perspectives, including:

. Unambiguous formulation of a DE.

. Qualitative and quantitative properties of solution of a DE.

. Analytic and numerical techniques.

. Application areas.

. Examples, some sample code and pointers to relevant applications.



In short, this is a rigorous, and at the same time practical introduction to an important branch of mathematics. We now describe these topics in more detail.

An optional “end-of-term” student mini-project is supported. It is up to the student to decide on this.
Daniel Duffy has been external supervisor for MSc/MFE computational finance theses in the last ten years (for example University of Birmingham, UCB, Baruch NYC etc.)



Global overview of ODE/PDE course

Online Courses :: Datasim



History of PDE in Finance 2000-2020

Login



Modules of ODE/PDE course in detail

https://www.datasim.nl/application/...dinary_and_Partial_Differential_Equations.pdf



Originator and personal Student Coach for this Course

Dr. Daniel J. Duffy is founder and owner of Datasim Education BV (founded 1989), which was one of the first pioneering companies to promote C++, object-oriented programming, system design and training in a range of industries such as telecommunications, Computer-Aided Design (CAD), holography (optical technology), process control, manufacturing systems and computational finance. In particular, these applications were designed using a combination of domain architectures (Duffy (2004)) and the famous design patterns that became popular in the early 1990s.

He is also the originator of two major and market leader C++ courses in cooperation with Baruch College, NYC (ranked #1 MFE school in 2023) and Quantnet Inc. (www.quantnet.com):

C++ Programming for Financial Engineering

Advanced C++ and Modern Design



These courses are taken by many professionals and MSc/MEF students in forty countries and on five continents. Student testimonials:



C++ Online Programming Cert Testimonials



Daniel Duffy is an internationally known author, trainer and numerical analyst. He has written more than ten books on programming, mathematics and computational finance. He has a PhD in mathematics (PDE/FDM) from the University of Dublin (Trinity College), much of which he uses in daily work and algorithms.

Testimonials

Testimonials :: Datasim





For (prospective) MFE students it is sufficient to do parts A,B,F and G (including exercises) are sufficient for your certificate because the topics are the foundations for ODE/PDE in finance. Of course, we also support the other modules if you have time to take them. In general, it normally takes between two and three months to complete parts A,B,F and G.

The standard company price per course is Euro 2395 per attendee. The discount price is Euro 1500 if you are a student or paying for yourself. All prices are exclusive of VAT (no VAT outside EU). If you have any other queries, for example on-site courses and group schemes, please contact me Daniel Duffy dduffy@datasim.nl



Follow-on courses

Applied Numerical Methods


https://www.datasim.nl/onlinecourses/101/distance-learning-applied-numerical-methods



Finite Difference Method


https://www.datasim.nl/onlinecourse...-difference-method-fdm-for-odes-pdes-and-sdes



The book Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach, March 2022.

https://www.wiley.com/en-gb/Numeric...l+Equation+(PDE+FDM)+Approach-p-9781119719670



Testimonials

Testimonials :: Datasim
 
Here is a nice example of a student project based on the current material.
 

Attachments

  • thesis.pdf
    274.3 KB · Views: 122
The physics of the lawn game Croquet.

And it's modelled by an ordinary differential equation (ODE). Of course.
 

Attachments

  • 101. Croquet.pdf
    1 MB · Views: 20
  • 124802288.0upBH5Qq.anaverna6sml.jpg
    124802288.0upBH5Qq.anaverna6sml.jpg
    590.4 KB · Views: 7
What are the prerequisites for this course?
"For whom is the Course and what are the Prerequisites?

This course is suitable for professionals in industry and finance as well as for advanced undergraduate and MSc/MFE students. The prerequisite knowledge is calculus to the level in the book by D.V. Widder 1989 Advanced Calculus Dover, for example. It is also an advantage if you are exposed to applications in which differential equations play a role or if you are writing a thesis in which they are needed.

The level of the course is similar to that in second and third year university courses in applied mathematics and engineering, for example. The main difference is that this focused course is dedicated to differential equations and their applications.

If you have any queries please do not hesitate to contact me, Daniel Duffy dduffy@datasim.nl to discuss the course."


 
Last edited:
MATT ROBINSON

This thesis introduces and elaborates on how to approximate option and bond price sensitivities (Black Scholes and Cox-Ingersoll-Ross (CIR) models) in a variety of ways. In general, option price depends on time and on the underlying stock variables as well as on a number of parameters such as volatility, interest rate and strike. The rate of change of the option price with respect to these quantities is computed (in the main, the first and second derivatives).

The thesis discusses a wide range of techniques to compute sensitivities. For example, if an analytic expression for the option is known then we can differentiate the formula or we can apply the Complex Step Method (CSM) to compute the sensitivity. Another popular method is Automatic Differentiation (AD). Continuing, it is possible to discretize the PDE to compute an approximate option price as an array and from there compute option delta and gamma using divided differences or cubic splines. For other sensitivities (such as vega, for example) this approach does not work and then the Continuous Sensitivity Equation (CSE) method is used which allows us to write the sensitivity as the solution of an initial boundary value problem for a Black-Scholes type PDE. The student also discovered new research topics as the project progressed such as well-posedness of the PDEs resulting from CSE and cases in which a PDE can have multiple solutions.

 
Just a bump
Online ODE PDE Course

Ordinary and Partial Differential Equations with Applications to Computational Finance

Dr. Daniel J. Duffy (Datasim Education BV) dduffy@datasim.nl

May 2023



Ordinary and partial differential equations (ODE/PDE) have major applications in many areas of science, engineering and computational finance and other important application areas. It is a huge area and it is difficult to know where to start if you wish to learn this subject matter. To this end, this focused, hands-on online course introduces the most important concepts, models and methods to get you up to speed as soon as possible.

Our (unique) approach is to examine differential equations (DEs) from several perspectives, including:

. Unambiguous formulation of a DE.

. Qualitative and quantitative properties of solution of a DE.

. Analytic and numerical techniques.

. Application areas.

. Examples, some sample code and pointers to relevant applications.



In short, this is a rigorous, and at the same time practical introduction to an important branch of mathematics. We now describe these topics in more detail.

An optional “end-of-term” student mini-project is supported. It is up to the student to decide on this.
Daniel Duffy has been external supervisor for MSc/MFE computational finance theses in the last ten years (for example University of Birmingham, UCB, Baruch NYC etc.)



Global overview of ODE/PDE course

Online Courses :: Datasim



History of PDE in Finance 2000-2020

Login



Modules of ODE/PDE course in detail

https://www.datasim.nl/application/...dinary_and_Partial_Differential_Equations.pdf



Originator and personal Student Coach for this Course

Dr. Daniel J. Duffy is founder and owner of Datasim Education BV (founded 1989), which was one of the first pioneering companies to promote C++, object-oriented programming, system design and training in a range of industries such as telecommunications, Computer-Aided Design (CAD), holography (optical technology), process control, manufacturing systems and computational finance. In particular, these applications were designed using a combination of domain architectures (Duffy (2004)) and the famous design patterns that became popular in the early 1990s.

He is also the originator of two major and market leader C++ courses in cooperation with Baruch College, NYC (ranked #1 MFE school in 2023) and Quantnet Inc. (www.quantnet.com):

C++ Programming for Financial Engineering

Advanced C++ and Modern Design



These courses are taken by many professionals and MSc/MEF students in forty countries and on five continents. Student testimonials:



C++ Online Programming Cert Testimonials



Daniel Duffy is an internationally known author, trainer and numerical analyst. He has written more than ten books on programming, mathematics and computational finance. He has a PhD in mathematics (PDE/FDM) from the University of Dublin (Trinity College), much of which he uses in daily work and algorithms.

Testimonials

Testimonials :: Datasim





For (prospective) MFE students it is sufficient to do parts A,B,F and G (including exercises) are sufficient for your certificate because the topics are the foundations for ODE/PDE in finance. Of course, we also support the other modules if you have time to take them. In general, it normally takes between two and three months to complete parts A,B,F and G.

The standard company price per course is Euro 2395 per attendee. The discount price is Euro 1500 if you are a student or paying for yourself. All prices are exclusive of VAT (no VAT outside EU). If you have any other queries, for example on-site courses and group schemes, please contact me Daniel Duffy dduffy@datasim.nl



Follow-on courses

Applied Numerical Methods


Online Courses :: Datasim



Finite Difference Method


Online Courses :: Datasim



The book Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach, March 2022.

https://www.wiley.com/en-gb/Numerical+Methods+in+Computational+Finance:+A+Partial+Differential+Equation+(PDE+FDM)+Approach-p-9781119719670



Testimonials

Testimonials :: Datasim
just a bump. Course open, as always.
 
Last edited:
It looks like a great way to expand the knowledge I'll get in my current course. We have covered good portions of A-C so far, but there seems to be a broader range of topics covered here and they look pretty fun.

I might be taking this and the follow ups at some point, the question is when. The Advanced C++ course will come first though. What order do you recommend? I think I've seen you point people who have completed the fist C++ course to the Numerical methods course, and I don't appear to be lacking anything needed for either the NM or FDM courses. I suppose it is buyers choice.
 
All you wanted know about parabolic PDE
(originally in Russian Mathematical Survey 1962)

Learn this and will then be few PDEs that intimidate you.
 

Attachments

  • A_1013156322602.pdf
    1.2 MB · Views: 17
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