The current price of a stock is $ 54.61 and the annual effective risk-free rate is 7.0 percent.

The current price of a stock is $ 54.61 and the annual effective risk-free rate is 7.0 percent. A call option with an exercise price of $55 and one year until expiration has a current value of $ 11.37 . 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.

Expert Solution

Put Call Parity Theorm:

It shows the long term equilibrium relation between Value of call with certain exercise price, Value of put with same exercise price, excercise price, exercise date and stock price today.

Vc + PV of Strike Price = Vp + Stock price

Vc = Value of call
Vp = Value of Put

Particulars	Values
Vc	$ 11.37
Strike Price	$ 55.00
Int rate	7%
Maturity Period in Year	1.0000
Stock Price	$ 54.61

Vc = Value of Call
Vp = Value of Put

Vp = Vc + PV of Strike Price - Stock Price

Computation of PV of Strike Price

PV of Strike Price = Strike Price * e^-rt
e - Exponential factor
r - Int Rate per anum
t - Time in Years
= $ 55 * e^-0.07 * 1
= $ 55 * e^-0.07
= $ 55 * 0.9324
= $ 51.28

Vp = Vc + PV of Strike Price -Stock Price
= $ 11.37 + $ 51.28 - $ 54.61
= $ 8.04

Value of Put = $ 8.04.

jeff jeffy answered 2 years ago

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