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Up: 6.1 American stock options
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6.1.3 Application
[ SLIDE
Put(CBOE) || same
VIDEO as previous section:
modem -
LAN -
DSL
]
Using your intuition for the parameters describing the price of an American
option, we are ready to use the VMARKET applet and compare the
numerical solution with market prices. Take the
American put
from
Cisco
that expired on Jan 18, 2003 with a strike at USD 20.
About half a year before the option expiry date (data from Aug 12, 2002,
i.e. 159/360 = 0.44 year before), the underlying share was trading for USD
13.12
with a market volatility around
60%
(follow the links to obtain current market data).
Under reasonable assumptions of a 3% spot rate from the US Treasury
and no dividend payed for that share, the VMARKET applet
below calculates the fair price using the
Black-Scholes model with an American exercise style.
VMARKET applet: press Start/Stop
to run the simulation until it stops about half a year before the
option expires.
For an approximative solution, you may simply click inside the plot
area to measure the payoff V(S) around the coordinate 13.12.
For a complete printout of the numerical solution, switch from
Double-click below in the applet to Print data to console,
set TimeStep=0. and press Step 1;
the number output can be now read from the Java-console (with Netscape
open Communicator->Tools->Java console) where x[]
is the price of the underlying, f0[] is the final condition
in grey and f[] the solution in black.
Don't forget to switch back to Double-click below avoiding
to overflow the Java console...
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After interpolation, the value obtained (USD 7.104) is very close to
the value that was quoted on the
Chicago Board of exchange
CBOE (USD 7.10).