Numerical Methods in Finance

Numerical methods in finance turn pricing models into prices. Almost no product beyond a plain European option has a closed-form price under a realistic model, so desks rely on simulation, finite differences, lattices and Fourier transforms, and on the calibration routines that fit models to the market. This course teaches those methods and how to know when they are wrong.

Why does error analysis matter so much?

Because a pricer that converges slowly, or not at all, still prints a number. A Monte Carlo price without a confidence interval, or an explicit finite-difference scheme run outside its stability limit, can be badly wrong without any warning. Each unit pairs a method with the checks that show whether it can be trusted.

How is the course taught?

Audio lessons give the reasoning, explainer films show the methods converging and failing, and the workbooks carry derivations, notebooks and cheat sheets. Assignments and the project receive written feedback from the faculty.

Who is this course for?

Quants heading for pricing, model validation or risk roles.

What you will be able to do

• Price options by Monte Carlo and reduce the variance with antithetic, control-variate and quasi-random methods.
• Solve the Black-Scholes equation with explicit, implicit and Crank-Nicolson schemes and judge their stability.
• Price under Heston and other models with Fourier methods.
• Calibrate a model to market prices and diagnose a poor fit.

Syllabus, module by module

1. Error, stability and cost

   Floating point, truncation error, convergence order and how to measure each.

2. Monte Carlo

   Path simulation, discretization of SDEs, confidence intervals and Greeks by simulation.

3. Variance reduction

   Antithetic variates, control variates, importance sampling and quasi-random sequences.

4. Finite differences

   Explicit, implicit and Crank-Nicolson schemes, boundary conditions and American exercise.

5. Trees and Fourier methods

   Binomial and trinomial lattices; characteristic functions and the FFT and COS methods.

What every course contains

Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.

1. Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
2. Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
3. Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
4. Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
5. Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
6. Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
7. Transcript. A full transcript of every film and every audio recording, searchable and quotable.
8. Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
9. Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
10. Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.

How the certificate is earned

Graded computational assignments and a final project: a pricer for one exotic option by two methods, with a written error analysis. On a pass you receive the Course certificate in Numerical Methods in Finance, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. Read how certification works.

Before you start

Stochastic calculus and the Black-Scholes model at the Institute's level, and confident Python.

• Stochastic Calculus and Stochastic Differential Equations
• The Black-Scholes Model and the Option Greeks