Consider IBM LEAPS at the close of trading for the
week ending November 22, 1996.
Assume for this example the dividend yield is a constant
continuous rate equal to 0.896% and the expiration is the Saturday
after the 3rd Friday of the contract month. The close
of IBM was 158.625 and other relevant numbers are in the table
below:
Tutor Break: Using Option Risk Management to examine decay
in a butterfly spread
Step 1: Select the Option Risk Management subject in
Option Tutor. Three windows open. Enter the data from the above
table into the Portfolio Window.
Hint: Be sure to save your work if you are using a complicated
data set. You can save to a file or you can copy and paste to
and from a spreadsheet.
Step 2: Click on "Plot Exposure" You can re-scale
as desired. For the current example this is from 100 to 200 for
the X-axis (the price of IBM stock). The Y-axis, the value of
the butterfly spread, is plotted from -10 to +5. In the Action
Window Profit Diagram and Price Exposure are selected.
The View 0 defines the present. You can scroll this from 0 to
1.15342 to go from present time to terminal payoff in the current
example. You can see that this does not look much like the classic
butterfly spread at the present time zero. But lets look at
the decay properties for this strategy:
Step 3: Scroll the view period to trace out the predicted
path of decay.
Hint: A color and line thickness change was made for the
last two clicks (time 1.141, 1.153). This illustrates how close
it is until maturity that the butterfly fully spreads out. You
can change color and line thickness by selecting the menu item
Options, Colors. Next by clicking on the label Portfolio Payoffs
and a line thickness choice will appear. This can be scrolled
to the desirable thickness level.
You can see from this graph that the classic shape of the butterfly
is due to decay. In addition, the largest part of the decay effect
is when the time to maturity is very small (analytically 1/square
root of time to maturity has a large effect on decay patterns).
By using Option Tutor's Option Payoffs subject you can look at the behavior of any option trading strategy at the time of expiration. In addition, by using the Risk Management subject you can look at the predicted path of a trading strategy to its terminal payoff diagram. This prediction is based upon the Black Scholes model for European options or a numerical solution obtained from the trinomial option pricing model for an American option.
(C) Copyright 1997, OS Financial Trading System