Question

5. We have we have the following information for a call and a put option on XYZ stock. Exercise price: $100 Call option price: $7 Put option price: $5 Risk-free rate: 8% Current market price of XYZ: $97 Time to maturity: 0.5 years Calculate the mispricing and show the arbitrage process if stock price closes at 80

Answer 1

Put Call Parity Equation

C+X/(1+r)^t=S0+P

C=Call premium

P=Put premium

X=Strike price of Put and Call

r=annual interest rate

t=Time in years

S0=Initial price of underlying

In this case,

Call option price appears to be very high, since it is out of the money call.

Considering Put Option premium given as $5, let us calculate amount of Call premium as per PUT CALL PARITY.

P=Put Premium=$5

X=Strike Price=$100

r=annual interest rate=8%=0.08

t=0.5 years

S0=Initial Price=$97

C+$100/(1.08^0.5)=$97+$5=$102

C=$102-($100/1.03923)=$102-$96.23=$5.77

The Call Premium should $5.77

In this case the Call Option is overpriced by (7-5.77)=$1.23

Arbitrage Process:

Short Call Option and Long Put Option

If we short on call option , we get $7

Cost of buying one put option =$5

Net amount received =($7-$5)=$2

Pay off at expiration:

Price at expiration =$80

Strike Price=$100

Payoff on Call Option =$0

Payoff on Put Option =($100-$80)=$20

Total Gain=$20+$2=$22