From: John Conover <john@email.johncon.com>
Subject: Option and Deriviative pricing.
Date: Tue, 26 Mar 1996 00:53:54 -0800
Hi Wendell. If you can, you might want to get the IEEE "Computational
Science and Engineering," Spring, 1996. There is an article,
"Computation Methods in Finance: Option Pricing," Emilio Barucci and
Leonardo Landi, Universita di Firenze, Umberto Cherubini, Banca
Commerciale Italiana. The article mentions Black-Scholes formula, and
then solves the partial differential equation with Feynman-Kac's
theorem, and then show that there is empirical evidence that a stock's
value can be modeled by a such a diffusion process, (of the log-normal
variety.) And not only that, they show that there is an optimal
option strike price that can be hedged with derivatives, to make the
option risk free.
They start with a simple fixed duration European option, then extend
the concept to an American option, complete with taxes and transfer
fee. What's interesting is that a lot of concepts from quantum
mechanics, 1/f phenomena, ie., shot noise, (Brownian noise is
mentioned as a model of the diffusion process-although it is not
stated, they really mean fractional Brownian, since it is a cumulative
sum on a process of a random variable with a normal distribution,
which they state early in the article-ie., it is a fractal.) They then
model things with neural networks, (actually, cellular automata,
implemented with a tree structure,) and offer some advanced analytical
tools using semi-nonparametric pricing through generalized Fourier
methods and wavelets. SOP in the information theory/communications
systems design and development business.
Whats interesting is that the authors have economics tenure, and they
are using the methodologies of sophomore and junior EE's. Maybe it is
time to start thinking about opening a 300 level class for EE's or
CS's in financial modeling and optimization of capital markets. The
introduction of Black-Scholes (which is relatively straight forward if
you understand PDE's-which I assume is the case by an EE's junior
year,) would be the only new concept-the rest is in the standard
curriculum by the junior level. Of course, you could run afoul of turf
battles with the Department of Economics, also.
John
--
John Conover, john@email.johncon.com, http://www.johncon.com/