The current price of a stock is $ 55.52 and the annual effective risk-free rate is...

The current price of a stock is $ 55.52 and the annual effective risk-free rate is 3.4 percent. A call option with an exercise price of $55 and one year until expiration has a current value of $ 12.80 . 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. Your Answer:

Expert Solution

Call Option:
Holder of call option will have right to buy underlying asset at the agreed price ( Strike Price). As he is receiving right, he needs to pay premium to writer of call option.He will exercise the right, when expected spot price > Strike Price. Then writer of option has to sell at the strike Price.

Put Option:
Holder of Put option will have right to sell underlying asset at the agreed price ( Strike Price). As he is receiving right, he needs to pay premium to writer of Put option.He will exercise the right, when expected spot price < Strike Price. Then writer of option has to buy at the strike Price.

Put Call Parity Theorm:

Vc + PV of Strike Price = Vp + Stock price

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^-0.03 * 1
= $ 55 * e^-0.034
= $ 55 * 0.9666
= $ 53.16

Vp = Vc + PV of Strike Price -Stock Price
= $ 12.8 + $ 53.16 - $ 55.52
= $ 10.44

Value of Put is $ 10.44

Pls comment, if any further assistance is required.

jeff jeffy answered 1 year ago

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