Taking the Ceiling out of Financial Analysis
Now, more than ever, financial computation involves more than pure
number crunching, and the new financial leaders are looking
to Mathematica for help.
Investment houses regularly "slice and dice" securities such as
mortgages, government bonds, and even junk bonds to meet specific
risk/return objectives. While spreadsheet programs and C/C++ remain
useful, symbolic programming languages--i.e., languages that
manipulate both the numbers and the symbols that represent the
financial structures--are increasingly needed to deal with the
increasing complexity of the financial world.
Dr. Ross Miller,1 one of the first
to take a symbolic approach to financial analysis,
used Mathematica to create a relatively simple model that is
traditionally numerical in nature: the Black-Scholes option pricing
model.
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"Mathematica makes it possible to
manipulate the Black-Scholes pricing formula directly as a symbolic
entity. This greatly simplifies computing the various risk
characteristics of an option--a task that is both tedious and
error-prone when performed in a more traditional manner--and
facilitates extensions of the model that are made 'on the
fly.'"
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Mathematica then helped pick up where the Black-Scholes
option pricing model left off. Although the Black-Scholes model
gives a closed-form solution for pricing European options, many
other options cannot be priced by this model. Such options include
American options and options whose terminal payoffs are dependent on
the path followed by the stock price. Using the binary and binomial
option pricing models and the Monte Carlo method, three financial
engineers2 used Mathematica to
price such options.
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"Without Mathematica, others have
had to use approximations to pricing formulas for options that are
difficult to price. Mathematica enabled us to price many of
these options directly."
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1. Dr. Ross Miller is the author of the
book Computer-Aided Financial Analysis and has published
several journal articles on information transfer in financial
markets and on the design of advanced electronic market systems. He
was the head of research for the National Westminster Bank and
served as a member of the technical staff of the General Electric
Corporate Research and Development Center before starting his own
consulting company specializing in investment and risk
management.
2. Simon Benninga, Raz Steinmetz, and John
Stroughair. Dr. Benninga is the author of Numerical Methods in
Finance, and his research interests include options and futures
markets. Raz Steinmetz and John Stroughair were graduate students at
the Wharton School of the University of Pennsylvania when this
research was conducted.
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