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A call option with a current value of $7.90. A put option with a current value...

A call option with a current value of $7.90. A put option with a current value of $7.60. Both options written on the same stock, with 1 year until expiration, and a strike price of $54.00. The prevailing risk-free rate is 5.00%. What must be the current price of the stock on which these two options are written? *** In your calculations, use simple discounting instead of continuous discounting. Also, do not enter the dollar sign and use two decimals (round off to 2 decimals).

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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.
Holder of calloption will exercise the right, when expected future spot price > Strike Price. Then writer of option has obligation to sell at the strike Price.
Holder will go for call option if he is bullish.

If the Future SPot Price > Strike Price - In the Money
If the Future SPot Price = Strike Price - At the Money
If the Future SPot Price < Strike Price - Out of the Money


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.
Holder of put option will exercise the right, when expected future spot price < Strike Price. Then writer of option has obligation to buy at the strike Price.
Holder will go for put option, if he is bearish.

If the Future SPot Price < Strike Price - In the Money
If the Future SPot Price = Strike Price - At the Money
If the Future SPot Price > Strike Price - Out of the Money


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

PV of StrikePrice = Strike Price / ( 1 + Int rate )

= $ 54 / ( 1 + 0.05 )

= $ 54 / 1.05

= $ 51.43

Stock Price = Vc + PV of Strike Price - Vp

= $ 7.90 + $ 51.43 - $ 7.60

= $ 51.73

Value of stock today is $ 51.73

jeff jeffy answered 1 year ago
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