Don't be fooled by
the title. This is a general introduction to financial engineering for a
mathematically sophisticated audience. It just happens to emphasize finite
difference methods. The authors are three mathematicians. It shows in both the
sophistication of the math and the lack of sophistication in the finance.
Finite difference
methods are something most often associated with the partial differential
equations approach to financial engineering, which is falling out of use. But
they can also be invaluable with the stochastic calculus approach. Some problems
are most easily solved by starting with the fundamental theorem of asset
pricing, translating the problem into a partial differential equation and then
applying finite differences.
Contents
1. Introduction
2. Basic options
3. Exotic options
4. Interest rate derivative securities
5. Basic numerical methods
6.
Initial-boundary value and LC problems
7. Free-boundary problems
8. Interest
rate modeling
This isn't
discussed in the book. It gets to finite difference methods exclusively via the
traditional Black-Scholes, partial differential equations approach. In this
respect, it reflects valid but dated ways of thinking.
The book is
clearly influenced by Wilmott, Dewynne and Howison (1993).
It doesn't cover some of the basics, such as partial differential equations, but
it does delve into more advanced mathematics. Wilmott et al is far better
written, but if you want to master the partial differential equations approach
to financial engineering, you might read Zhu et al as a supplement or follow-up. [11/16/05]
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