Question

1. A European call option was written on the non-dividend paying shares of firm X. The option has an exercise price of $65 and expires in 73 days. The underlying shares of firm X currently sell for $67.25 and the standard deviation of their continuously compounded returns is 23%. The annual riskless rate is 5.15%.

a.) Using the information provided, what is the value of d1, the value used for accessing the cumulative probability of a value of d or less?

Multiple Choice 0.482 0.269 -0.132 -0.119

b. Using the Black Scholes model, what is the value of the call option. Assume a 365 day year.

Multiple Choice $2.85 $4.34 $2.16 $3.14

c. Using the put call parity relationship, estimate the value of a put option with the same exercise and maturity as the call.

Multiple Choice $1.42 $3.53 $3.94 $3.06

Answer 1

	Call Option price=	SN(d1) - Xe-r t N(d2)
	d1 =	[ ln(S/X) + ( r+ v2 /2) t ]/ v t0.5
	d2 =	d1 - v t0.5
	Where
S=	Current stock price=	67.25
X=	Exercise price=	65
r=	Risk free interest rate=	5.15%
v=	Standard devriation=	23%
t=	time to expiration (in years) =	0.2000
d1 =	[ ln(67.25/65) + ( 0.0515 + (0.23^2)/2 ) *0.2] / [0.23*0.2^ 0.5 ]
d1 =	[ 0.034 + 0.01559 ] /0.102859
d1 =	0.482405
d2 =	0.482405 - 0.23 * 0.2^0.5
	0.379546
N(d1) =	N( 0.482405 ) =	0.68524
N(d2) =	N( 0.379546 ) =	0.64786
Option price=	67.25*0.685-65*(e^-0.0515*0.2) *0.648
	4.40

Put call parity
P = Xe-rt -S +C
Xe-rt =	$   64.33
-S =	$ (67.25)
C =	$      4.40
P =	$      1.49

a: 0.482

b. $4.34 (nearest)

c. $1.42 (nearest)

Please rate.