Question

1. If the price of a given European call on a non-dividend paying stock is lower than its theoretical value, explain in detail how you can use the put-call-parity c + Ke^-rT = p + S₀ to generate an arbitrage gain.

Answer 1

Answer-

Put-Call-Parity relation is

C+ Ke-rT = P + S0

C = Call Option Value
P = Put Option Value
S0 = Initial price of underlying stock
K = Strike price
r = annual interest rate
T = Time in years
Ke-rT = Present value of strike

When European call on a non-dividend paying stock is lower than its theoretical value then the value C is lower and ttherefore the value of the LHS of Put-call parity equation C+ Ke-rT is less than the RHS of the Put call parity P + S0 as C value is lower.
Therefore there is an arbitrage gain when the LHS and RHS are not equal and the arbitrage gain will be equal to the difference of ( P + S0 ) - ( C+ Ke-rT ) .