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A Trader’s Guide to PDE Methods


Objective: a comprehensive programme available as a fully customisable in-house seminar providing the background and tools for traders, structurers, and risk managers to build and use methods such Finite Difference and Finite Elements to solve complex derivatives valuation and risk problems.  

Please note that though this is necessarily a quantitative topic, the presentation is intended for "front office" application, and so the language and the rigour of the presentation is geared towards market professionals, rather than mathematicians.


·        Market maker, prop traders, structurers

·        Risk Management

Table of Contents

This is a fully customisable programme that may include any and all aspects as you require, and the following is only an illustration of one of the possibilities.

1)     Overview: The “big picture” introduction partial differential equations (PDEs), what they mean, where they come from, and their relationship to "modelling" market dynamics and securities/derivatives trading.   This section also summarises the key issues and methods for PDEs, and starts to lay the foundation for the selection of the "right" method for the "right" job.

2)      Finite Difference Basics 1: introduces the basic ideas driving the FD method, and the Black-Scholes PDE is used to develop both and explicit and implicit FD simulator and their usage criteria - including source code and Windows calculator.

3)      Finite Difference Basics 2: introduces additional features that may be employed with FD to obtain "improvements" of various forms, and includes concepts such as up-streaming, non-uniform grids and mesh refinement issues, "time weighting" (e.g. Crank-Nicholson), and rules for the use of such in practice.  This section also introduces the methodology use a single FD simulator to solve virtually any valuation problem.

4)     Finite Difference Advanced: covers more complex issues such as non-linear problems (e.g. which may arise when accounting for transactions costs), more complex models such as term-structure effects, and exotic options, multi-factor/multi-asset valuations.

5)     Finite Element Basics 1: review of variational concepts as the underpinnings of the FE methodology, and developing an FE implementation of the Black-Scholes problem. 

6)     Related Methods and Implementation: focuses on issues for real world implementation of large scale valuations, and consideration of methods related to numerical PDE solvers such as linear algebra issues for the Ax=B problem with review of direct, iterative, and  multi-grid methods, as well as conditioning methods such Choleski pre-conditioned conjugate gradient approach.

7)     Comparison of Methods:  analyses the pros and cons of different PDE methods such as FD, FE, Boundary Methods, etc, as well as other numerical methods (e.g. trees. Monte Carlo, etc) not only by comparing valuation and risk results, but also by examining  their relevance to trading problems, and also providing insight into the relative cost of building, maintaining, and using such methods.


820 Pages of comprehensive and extensively illustrated Handout Notes (see samples here)

Plus copies of relevant TG2 Books/e-Books

Note: Seminars can be tailored to your trading, risk, client, and systems needs.  Submit your needs, and/or "cut/paste" from other Seminars (see entire "standard" list HERE)

    Get a Syllabus in more detail

    Sign Up for a scheduled course

    Sign Up for an in-house course


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Last modified: July 25, 2011