Ch. 15-09 Build a Model Solution									3/6/2001
Chapter 15. Solution to Ch. 15-09 Build a Model
Assume you have been given the following information on Purcell Industries:
	P	$15		X	$15
	t	0.5		r	10%
	s2	0.12
Using the Black-Scholes Option Pricing Model, what would be the value of the option?
First, we will use formulas from the text to solve for d1 and d2.
					Hint: use the NORMSDIST function.
	(d1)	=	0.327	N(d1) =	0.628014260962472
	(d2)	=	0.082	N(d2) =	0.532537344178941
Using the formula for option value and the values of N(d) from above, we can find the call option value.
	V	=	$1.822
a. Construct data tables for the intrinsic value and Black-Scholes formula value for this option, and graph
this relationship. Include possible stock price values ranging up to $27.
			Option Value
		Current	Intrinsic	B-S formula
	Exercise	stock	Value	Value	Option
	Price	price	$0	$1.822	Premium
	$15.00	$1.00	$0.00	$0.00	$0.00
	$15.00	$3.00	$0.00	$0.00	$0.00
	$15.00	$6.00	$0.00	$0.00	$0.00
	$15.00	$9.00	$0.00	$0.03	$0.03
	$15.00	$12.00	$0.00	$0.45	$0.45
	$15.00	$15.00	$0.00	$1.82	$1.82
	$15.00	$18.00	$3.00	$4.09	$1.09
	$15.00	$21.00	$6.00	$6.83	$0.83
	$15.00	$24.00	$9.00	$9.76	$0.76
	$15.00	$27.00	$12.00	$12.74	$0.74
c. Suppose this call option is purchased today, draw the profit diagram of this option position at expiration.
	XCALL =	$15
	if P= …	Call
	$1	-$1.82
	$3	-$1.82
	$6	-$1.82
	$9	-$1.82
	$12	-$1.82
	$15	-$1.82
	$18	$1.18
	$21	$4.18
	$24	$7.18
	$27	$10.18