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
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