Question

The current price of a stock is $50, the annual risk-free rate is 6%, and a 1-year call option with a strike price of $55 sells for $7.20. What is the value of a put option, assuming the same strike price and expiration date as for the call option? Select one: a. $7.33 b. $7.71 c. $8.12 d. $8.55 e. $9.00

Answer 1

The value of the put option is;

e. $9.00

Step-by-step explanation:

To determine the value of the put option can be expressed as;

C(t)-P(t)=S(t)-K.e^(-rt)

where;

C(t)=value of the call at time t

P(t)=value of the put at time t

S(t)=current price of the stock

K=strike price

r=annual risk free rate

t=duration of call option

In our case;

C(t)=$7.2

P(t)=unknown

S(t)=$50

K=$55

r=6%=6/100=0.06

t=1 year

replacing;

7.2-P=50-55×e^(-0.06×1)

7.2-P=50-(55×0.942)

7.2-P=50-51.797

P=51.797+7.2-50

P=$8.997 rounded off to 2 decimal places=$9.00