Final answer:
The Put-Call Parity relationship c + Ke-rT = p + S0 is a fundamental concept in finance that relates the prices of European call and put options with the same strike price and maturity, based on arbitrage arguments.
Step-by-step explanation:
The equation c + Ke-rT = p + S0 is known as the Put-Call Parity relationship in finance. This equation provides a relationship between the price of a European call option (c) and a European put option (p) on the same underlying asset with the same strike price (K) and time to maturity (T). It incorporates the current price of the stock (S0) and the risk-free interest rate (r).
To prove the Put-Call Parity, we can construct two portfolios that will have the same payoff at time T. Portfolio A consists of one European call option and an amount Ke-rT invested in a risk-free bond that will grow to K at expiry. On the other hand, Portfolio B consists of one European put option and one stock.
At the time of expiration T, the value of Portfolio A will be either K or ST (whichever is higher, because the call option will only be exercised if it's in the money). Similarly, the value of Portfolio B will also be either K or ST (as the put option will ensure that the holder can sell at strike price K if the stock price is lower). By arbitrage-free argument, both portfolios must have the same value today, which is how we derive the Put-Call Parity formula c + Ke-rT = p + S0.