From: John Conover <firstname.lastname@example.org>
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, email@example.com, http://www.johncon.com/