Upscale --
Two guys received the Nobel Prize for answering this question: Robert
Merton and Myron Scholes:
American Mathematical Society
"1997 Nobel Prize in Economics"
http://www.ams.org/new-in-math/nobel1997econ.html
The model used by the financial industry since the early 1970s is the
Black-Scholes option pricing model, named for Myron Scholes and
Fischer Black, who died in 1995. They developed the model while
teaching at the University of Chicago Graduate School of Business in
the early 1970s.
Though it's been the subject of much debate -- academic, mathematical
and real world -- it's used in computer models to price options around
the world. Traders look for arbitrage based on inefficiencies in the
market. And, the employment of option theory goes way beyond that,
but I'm getting off-topic now.
THE PRICE
==========
The answer to your question, "What would be a fair sale price?" is:
$37.70 - $37.85
BLACK-SCHOLES MODEL
========================
Prof. Kevin Rubash, at Bradley University, has a page on the
Black-Scholes model that is both simple yet complete. It includes a
history of options pricing theory and a links to a pair of calculators
on other websites, though one of the two links goes to a specialized
software package for option pricing.
Foster College of Business Administration
"A Study of Option Pricing Models" (Rubash, undated)
http://bradley.bradley.edu/~arr/bsm/model.html
Option prices are determined, as you're aware, by the difference
between market value of the stock and strike price, but also by:
? market volatility: the more volatile the OVERALL stock market is,
the higher the value. After the Sept. 11, 2001 terrorist attacks the
overall market volatility increased in option prices. With a country
at war, running a huge budget and trade deficit, volatility is likely
to increase as interest rates go up. That will effect the FUTURE
value of an option, but it's usually discounted in "steady" markets
and should effect your price here.
? stock volatility, often expressed in terms of beta. This is one of
the most-important factors, as you know from IPO volatility -- though
a "beta" for volatility of a stock is usually calculated over at least
1 year of trading. Normally, you could base a publicly-traded
company's volatility on the betas of others in their business segment
-- though even then factors like capitalization can made this a very
debatable measure. Luckily the model we've used allows you to change
your assumptions on volatility -- but to get that price range we've
assumed 25% in price volatility in the next 2 years.
* interest rates. Black-Scholes original model specified "risk-free"
rate, which would be a 5-year Treasury bill for this example. Some
have argued that the interest rate should be the broker loan rate, as
it is closer to the real-world cost of "carrying" an option. Since
the prime rate today and the 5-year T-bill are both 4.0%, I've assumed
4.0%
* time left on the option.
Here's Prof. Rubash's summary of the Black-Scholes model, including
its assumptions. Don't worry too much about the assumptions, as tests
have shown that European and American options (which have VERY
different expiration terms) are close in value in an efficient, openly
traded market:
Bradley University
"The Black and Scholes Model" (Rubash, undated)
http://bradley.bradley.edu/~arr/bsm/pg04.html
Links to the Numa calculator that I used here. This is a particularly
nice calculator because it gives you a range of volatility options and
the impact on the pricing:
Numa Financial Systems
Option Pricing Calculator
http://www.numa.com/derivs/ref/calculat/option/calc-opa.htm
An alternate valuation can be pulled from any of Peter Hoadley's
"Option Strategy Analysis" tools and you'll find a similar result:
Hoadley.net
"On-Line Options Pricing & Probability Calculators" (Hoadley, undated)
http://www.hoadley.net/options/calculators.htm
Many investment pages allow you to calculate a normal American option
using the Black-Scholes model -- and some have ACTUAL market option
pricing:
Schaeffer's Research
"Option Pricing Calculator"
http://www.schaeffersresearch.com/streetools/options/calculator.aspx
The Google search strategy following is very good for coming up with a
range of discussions, from real-world use to web-based calculators to
academic discussion of option pricing:
"Black-Scholes" + "option pricing"
Best regards,
Omnivorous-GA |
