Question

6. [Call option value] A one-year call option contract on SUNNY Co. stock sells for $845. In one year, the stock will be worth $64 or $81 per share. The exercise price on the call option is $70. What is the current value of the stock if the risk-free rate is 3%? (Note that one contract involves 100 shares of stock)

Answer 1

Assume, Current Value=X

It can go up =U=$81

It can go down=D=$64

Probability of going up=p

Probability of going down=1-p

Call strike price=$70

Assume ,we buy (long)D Shares and Sell(short) one call option.

Payoff on shorting   one Call option,if the share price goes up to U=$81:

(70-81)=-$11

Value of D shares=D*81

Payoff of shorting one Call option , if shares goes down to D=$64,

Payoff on option =$0

Value of D shares=D*64

Portfolio is riskless if,

D*81-11=D*64+0

17*D=11

D=11/17=0.647059

Riskless portfolio :

Long 0.647059 shares and short 1 Call Option

Value of portfolio in one month:

81*0.647059-11=$41.41

Value of Portfolio today=41.41/(e^r)

r=Risk Free interest rate=3%=0.03

Value of the portfolio today=41.41/(e^0.03)=$40.19

Value of Share=0.647059*X

Value of Option =$845/100=$8.45=0.647059*X-$40.19

0.647059*X=$8.45+$40.19=$48.64

X=$48.64/0.647059=$75.17

Current Value of the Stock

$75.17