Put Call Parity

Summaries

Just a summary, for details, please refer to:

http://minute-class.com/?p=62

http://minute-class.com/?p=59

http://minute-class.com/?p=61

1. Fiduciary Call
1. Long Bond (matured at T with X value)
2. Long European Call (Striking price X, expire at T)
3. Future value of the portfolio (X if out of money, S(T) if in the money) *** no need to consider premium because we are talking about the value of the portfolio at T, not how much you earn
2. Protective Put
1. Long Put (Striking price X, expire at T)
2. Long Stock (Any current price)
3. Future value of the portfolio (X if in the money, S(T) if out of money)
3. Out of money of Protective Put is just in the money of Fiduciary call. Since the future values of them the same, so the current costs have to be the same. This is call put-call parity:

X/(1+rf)^T + C0 = P0 + S0

Synthetic put option:

P0 = C0 + X/(1+rf)^T – S0

1)      long call option (X,T)

2)      buy discounted bonds with PV X/(1+rf)^T

3)      short a stock

Why use put-call parity to do synthetic put, call, bonds and stocks?

1)      to price them

2)      to gain arbitrage profit (Buy low, sell high)