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.
Audience:
·
Market maker, prop traders, structurers
·
Risk Management
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)
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