The current price of a stock is $ 51.84 and the annual risk-free rate is 3.7 per

Question

The current price of a stock is $ 51.84 and the annual risk-free rate is 3.7 percent. A put option with an exercise price of $55 and one year until expiration has a current value of $ 6.25 . What is the value of a call option written on the stock with the same exercise price and expiration date as the put 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. Note, the given interest rate is an effective rate, so for calculation purposes, you need only discount the using the risk free rate, no e x adjustment is needed.

Explanation / Answer

Since both the put option and call option have the same underliner,same exercise price and same expiration,therefore the value of call option can be calculated using "Put call parity"

Put call parity is given by:

P + S = C + Present value of E

Where

P = Value of put

S = Current price of the stock

C = value of call

E = Exercise price

Therefore using the formula we get :

6.25 + 51.84 = C + Present value of 55

6.25 + 51.84 = C + (PVIF (3.7,1) * 55)

6.25 + 51.84 = C + 53.04

C = 5.05 (Ans)

Hence, the value of call option is 5.05.

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