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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...

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).