Question

Refer totable below, which lists the prices of various XXX Corp. options. Use the data in the figure to calculate the payoff and the profit/loss for investments in each of the following May 2021  (one year to maturity) expiration options on a single share, assuming that today share price is $20 and on the expiration date it will be $21.

		Cost	TimeValue	Payoff                Profit/Loss
a.	Call option, X = 18	2.80
b.	Put option,  X = 18	0.65
c.	Call option, X = 20	0.95
d.	Put option,  X = 20	0.85
e.	Call option, X = 22	0.55
f.	Put option,  X = 22	2.75

-What must be risk free interest rate to justify call-put parity for options with strike price X=20

Answer 1

Options gives a right but not an obligation to the holder to buy or sell an asset at a certain date at a certain rate

Payoffs

Call payoff = (Spot Price - Strike Price ) (Where S>X) or Zero (Where S<X)

Put Payoffs = (Strike Price - Spot Price)  (Where S<X) or Zero (Where S>X)

Profit / Loss = Payoff - Option Price

Put Call Parity

Put-call parity states that a fiduciary call should be equal to protective put. Fiduciary call means buying a call and investing in the PV of the strike price which ensures we have cash to buy the asset. Protective put is a position where we buy a put and we also buy a stock so that it limits the downside of a stock.

i.e Call + PV (Strike Price) = Put + Stock

i.e 0.95 + 20 / (1+R)^1 = 0.85 + 20

i.e 20/(1+R)^1 = 19.90

i.e 1.0050 = (1+R)

R = 0.50%