Question

# The current price of a stock is \$ 58.72 and the annual effective risk-free rate is...

The current price of a stock is \$ 58.72 and the annual effective risk-free rate is 7.8 percent. A call option with an exercise price of \$55 and one year until expiration has a current value of \$ 8.91 . What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Show your answer to the nearest .01. Do not use \$ or , in your answer. Because of the limitations of WEBCT random numbers, some of the options may be trading below their intrinsic value. Hint, to find the present value of the bond, you do not need to make the e x adjustment, simple discount at the risk free rate.

From the put call parity equation

c+ K/(1+r)^t = p+S

where c and p are call and put option premiums respectively, c= \$8.91

K is the strike price of the options =\$55

, r is the periodic interest rate = 7.8% p.a.

and t is the time period in years = 1

S is the spot price = \$58.72

So, we have p = c+ K/(1+r)^t - S = 8.91+ 55/1.078 - 58.72 = \$1.210408

So, the value of the put option is \$1.21 (assuming the stock did not pay any dividend during the one year)

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