An example, using stock options follows, though this may be generalised. Specifically consider a call option and a put option with the same strike K for expiry at the same date T on some share. Suppose the share has value S on expiration.

First consider a portfolio that consists of one put option and one share. This portfolio has value:

Now consider a portfolio that consists of one call option and K bonds that each pay (with certainty) at time T. This portfolio has value:

Notice that, whatever the final share price S is at time T, each portfolio is worth the same as the other. This implies that these two portfolios must have the same value at any time t before T. To prove this suppose that, at some time t, one portfolio were cheaper than the other. Then one could purchase (go long) the cheaper portfolio and sell (go short) the more expensive. Our overall portfolio would, for any value of the share price, have zero value at T. We would be left with the profit we made at time t. This is known as a risk-less profit and represents an arbitrage opportunity.

Thus the following relationship exists between the value of the various instruments at a general time t:

- C(t) is the time-t value of the call
- P(t) is the time-t value of the put
- S(t) is the time-t value of the share
- and B(t,T) is the time-t value of a bond that pays at T.

Using the above, and given the (fair) value of any three of the call, put, bond and stock prices one can compute the (implied) fair value of the fourth.

- Put-Call Parity, Riskglossary: http://www.riskglossary.com/articles/put_call_parity.htm
- Put-Call Parity Relationship, Quantnotes: http://www.quantnotes.com/fundamentals/options/putcallparity.htm