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1989-10-14
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THE OPTIONS CALCULATOR
Copyright (c) 1989 Philip Miller
v 2.01 ( 10-13-89 )
!**!**! DISCLAIMER !**!**!
THE OPTIONS CALCULATOR is provided to the user as SHAREWARE. Distribution
of this program without charge is encouraged. This program is provided
without warranty, implied or expressed. The author accepts no liability in
the use or application of this program. It is assumed by the author that
the user of this program has some knowledge of the trading of futures
options or INDEX OPTIONS such as the OEX or XMI INDICES and of the risk
involved in speculation.
Subjective or intuitive judgement based on experience is essential in
utilizing information derived from this program to achieve profits. Trading
futures or options on futures is a high risk affair!
The author accepts no liability or responsibility for losses suffered in
the futures or options market by the user. THE OPTIONS CALCULATOR is not a
trading system, nor does it guarantee future results or values.
See below for suggested further technical reading and information.
INTRODUCTION
This shareware program was written for you -- the options trader.
While there are many programs available to calculate index and stock option
premium values, most of the programs I have seen in the last few years are
cumbersome.
I strongly feel it is not enough "to get the numbers right". Successful
programs must have an appealing and easy-to-read screen format, which is
slightly different than the hackneyed expression, "user friendly."
In particular, this program like most commercial programs, "saves" the most
current values used so that you are not constantly asked to re-enter the
same values over and over again -- usually a most tedious, and unnecessary
task.
The program is based on the now familiar, Black-Scholes model, seemingly
used by most option modelers, although there are other models that have
been developed over the years.
Briefly, the Black-Scholes equation, published in 1973 and coincident with
the start of the Chicago Board of Options (CBOE), uses the following vari-
ables:
The current (or closing) OPTION PRICE
The STRIKE PRICE ( "out-of-the-money", "at", or "in-the-money" )
TIME TO EXPIRATION of the option ( options cease trading on the third
Friday and expire the following day on Saturday )
VOLATILITY of the strike price ( a measure of price movement in
relation to the underlying stock or index price).
RISKLESS RATE ( the 90 day T-Bill rate = a "riskless" investment )
It turns out that the most important variables are TIME and VOLATILITY.
TIME is always chipping away at the value of an option premium -- that is,
all other variables the same or even with a gently increasing underlying
index or stock price, time will have the effect of eroding the value of
your premiums. This marches at a logarithmic rate.
VOLATILITY is the other variable that in part determines the costliness of
a particular premium, the higher the volatility the higher the premium.
Call and put premiums may have quite different values, as is the case at
present.
SUGGESTED SET-UP
*** IT IS IMPORTANT TO NOTE ***
that once a volatility estimate has been entered, the premiums calculated
are most accurate only for THE STRIKE PRICE ENTERED. As the strike prices
diverge the values are only approximate and may vary significantly from
real values. The highlighted strike price, therefore, is the only price
that has real meaningful usefulness in terms of varying all other
parameters.
A suggested method of deriving fair market comparisons is as follows:
1. Enter the current or closing price in the first field.
2. Enter the nearest at-the-money ( nearest the actual index close ) value
in the second field. This is the value most likely to be fairly priced.
It is suggested that standard option codes be entered here although, as
discussed below ( OTHER FEATURES ), you can simply enter strike prices
directly.
3. Days to expiration will initially default to days from today and will
automatically include an exploding window calculator to change this
default. If you want to keep this value constant then you can toggle F6
to stop the exploding window on subsequent passes and the days to
expiration field will then remain constant.
4. Enter an approximate guess for the volatility or accept the default
values in the Volatility field.
5. Enter the current 3 month T-bill rate or accept the default value in the
rate field.
6. The program will now calculate the value of the premium given the above
parameters. You now have the option of entering the actual value from
the day's closing quotes ( or up-to-the-minute quotes ) or accepting the
calculated value of the premium. An iterative process in the program
will then calculate the implied volatility which is used as the
subsequent guess for volatility on the next pass. Incidentally, you will
see that the time premium is always greatest at-the-money.
Now you can get a fair estimate of premiums at various strike prices that
are "mispriced".
Alternatively, you can change any of these parameters according to your own
estimate or guess to calculate "what-if" scenarios such as:
- Given today's OEX 310 call, what would one most likely expect tomorrow's
310 call to be given an estimated closing or intraday index price.
- In a volatile market, how high or low would the OEX or XMI closing need
to be to achieve a targeted premium price for a given strike price.
- In a flat market, how will a premium price change over the next week or
two This will show the decay of the time premium alone.
THE PROGRAM
THE OPTIONS CALCULATOR is for the most part quite self-explanatory.
At the start of the program, values will already be available. These can
be changed within the specified limits of the program. You can step through
the values with the tab, down arrow, enter, or mouse down, mouse left
buttons. All of these will quickly step through the entry fields.
To see the effect of changing one variable such as time or volatility, just
enter the value and quickly step through the remainder of the fields. In so
doing you will see the effect of time and volatility variables in a much
more understandable fashion.
To exit the program properly requires <esc>, when prompted, following the
display of all seven strike value premiums. In doing so you will "save" all
parameters for the next session. If you want to exit prior to the above
you can simply press F10 and immediately exit without saving values. You
will also see the sign-off logo reminding you that great effort was
expended developing this program. The author would appreciate any and all
feedback.
By registering your copy you will have the satisfaction of knowing that
further good programs such as this will continue to be offered according to
the SHAREWARE concept.
The point is, registration is what SHAREWARE is all about.
OTHER FEATURES
The program will now display the results in either four-place decimals or
in 1/16 fractions for easier comparison to daily charted values. This is
accomplished by pressing F7.
There is more on-line help in this version by pressing F1 for help, F2 for
strike and month codes or F5 for a glossary of terms.
When prompted, you can toggle the CALLS or PUTS with F4 if using number
inputs in the Strike field. This allows you to calculate the CALL or PUT
premium if not set by the use of Standard Option codes.
In other words, using "VT" in the Strike field will give the October 300
PUT. All subsequent values will default to these parameters including all
values for PUTS. "JT" will give all the same values except all premium
values will be for CALLS.
If, alternatively, you input 300 in the Strike Field and enter 10 in the
expiration window for October, then when prompted in the premium field, you
can change to CALLS or PUTS by pressing F4 anytime prior to entering the
premium field.
The program will now run from any directory as long as it resides in a
directory that is accessed by the current path. The program reads all
default values from a block within itself and upon exiting rewrites these
values to the program file itself. This eliminates the need for a separate
data file as in v 1.01. As a result, you will see that the program date
and time attributes are constantly being changed and updated. This may not
work perfectly if using DOS v 2.xx.
Toggling F8 shows memory available
Immediate exit provided by pressing F10 key, so a whole is not necessary
nor is it necessary to ctrl-break out.
FUTURE RELEASES
Future releases will contain graph analyses to better see time premium
decay and other possible time and value outcomes.
FURTHER SUGGESTED READING
The following books are quite useful for more detailed and analytical dis-
cussions of the Black-Scholes pricing model. Some of these may be difficult
to locate outside of major metropolitan areas:
"Option Pricing and Strategies in Investing" by Richard M Bookstaber
An Addison-Wesley Professional Book
"Options As A Strategic Investment" by Lawrence G. McMillan
New York Institute of Finance, A Prentice-Hall Company
"Sure Thing Options Trading - A Money Making Guide to the New Listed
Stock and Commodity Options Markets" by George Angell
A Plume Book, New American Library
"The Pricing of Options and Corporate Liabilities" by F. Black and
M. Scholes, Journal of Political Economy, 1973, 81 (May): 637-654
( This is the original article for the Black-Scholes model )
TECHNICAL INFORMATION
This program is written in Turbo Pascal v5.5. Every effort to trap errors
at each entry point has been made. The program runs more smoothly the
faster the microprocessor speed ( CPU speed ) and is greatly enhanced with
the use of a co-processor ( 80287, 80387, etc ). It has been tested on an
AT clone at 10 MHz. On a vintage IBM PC the calculations will take a few
seconds to complete for data display.
All of the internal routines have been enhanced using TurboJock's Turbo
Toolkit(t) v5.01, a program that is worthy of high praise. Those interested
should look for this on local BBS services under TTT5 or similar file names.
RELEASE DATA
CALLS101 ( 8-24-89 )
- Straight forward calculation of premium prices.
CALLS201 ( 10-01-89 )
- Added the days to expiration window calculator so you know
exactly how many days to expiration without having to refer
to some other tedious source.
- Added the iterative process of calculating the implied volatility
which allows for more accurate pricing information. Uses a
"Secant" numerical method of iteration. The cryptic "its" value
refers to the number of iteration passes need to determine an
implied volatility.
- Shows the intrinsic and time premium values directly.
- Displays the full nature of the option in the middle of the screen
- Toggle between decimal or fraction display.
- Slightly different display showing the entered Strike Values in
high video and all other strike price values in low video.
- More help screens on-line including an on-line glossary of terms.
- Eliminated the CALLS.DTA file which contained the default values.
This has now been supplanted by a routine that saves the values
directly to the main program.
- Memory display window just for your information.
- Date and time are constantly displayed at top of screen.
- Allow for immediate EXIT with F10 key
FURTHER INFORMATION
All suggestions, complaints or compliments AND contributions in the amount
of TWENTY DOLLARS ( $20 ) may be sent to me at the following address:
Philip Miller
32680 Coast Ridge Drive
Carmel, CA 93923
or
CRICKET BBS
(408) 373-3773
MONTEREY, CA