Question

The price of Cilantro, Inc., stock will be either $70 or $90 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 6 percent. a. Suppose the current price of the company’s stock is $80.

What is the value of the call option if the exercise price is $60 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

) b. Suppose the current price of the company’s stock is $80. What is the value of the call option if the exercise price is $65 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Part A:

Risk Nuetral Prob to go upside ( P ):
P = [ e^rt - d ] / [ u - d ]
d = Down side price / Stock Price
u = Upside Price / Stock Price
e^rt :
= e^0.06 * 1
= e^0.06
= 1.0618

d = $ 70 / $ 80
= 0.875

u = $ 90 / $ 80
= 1.125

P = [ e^rt - d ] / [ u - d ]
= [ e^0.06 * 1 - 0.875 ] / [ 1.125 - 0.875 ]
= [ e^0.06 - 0.875 ] / [ 1.125 - 0.875 ]
= [ 1.0618 - 0.875 ] / [ 1.125 - 0.875 ]
= [ 0.1868 ] / [ 0.25 ]
= 0.7473

Risk Nuetral Prob to go Downside side (1 - P ):
1 - P = 1 - 0.7473
= 0.2527

Value of Call after 1 Year :

Future SP	Strike Price	Exercise/ Lapse	Prob	Value of Call	Expected Vc
$                                   90.00	$               60.00	Exercise	0.7473	$                30.00	$         22.42
$                                   70.00	$               60.00	Exercise	0.2527	$                10.00	$           2.53
Value of call after1 Years					$         24.95

Value of Call Today:
Value of call after 1 Years * e^-rt
= $ 24.946 * e^-0.06 * 1
= $ 24.946 * e^-0.06
= $ 24.946 * 0.9418
= $ 23.4933

Value of call is $23.49

Part B:

Risk Nuetral Prob to go upside ( P ):
P = [ e^rt - d ] / [ u - d ]
d = Down side price / Stock Price
u = Upside Price / Stock Price
e^rt :
= e^0.06 * 1
= e^0.06
= 1.0618

d = $ 70 / $ 80
= 0.875

u = $ 90 / $ 80
= 1.125

P = [ e^rt - d ] / [ u - d ]
= [ e^0.06 * 1 - 0.875 ] / [ 1.125 - 0.875 ]
= [ e^0.06 - 0.875 ] / [ 1.125 - 0.875 ]
= [ 1.0618 - 0.875 ] / [ 1.125 - 0.875 ]
= [ 0.1868 ] / [ 0.25 ]
= 0.7473

Risk Nuetral Prob to go Downside side (1 - P ):
1 - P = 1 - 0.7473
= 0.2527

Value of Call after 1 Year:

Future SP	Strike Price	Exercise/ Lapse	Prob	Value of Call	Expected Vc
$                                   90.00	$               65.00	Exercise	0.7473	$                25.00	$         18.68
$                                   70.00	$               65.00	Exercise	0.2527	$                   5.00	$           1.26
Value of call after1 Years					$         19.95

Value of Call Today:
Value of call after 1 Years * e^-rt
= $ 19.946 * e^-0.06 * 1
= $ 19.946 * e^-0.06
= $ 19.946 * 0.9418
= $ 18.7844

Value of call is $18.78

Pls comment, if any further assistance is required.