Put-call parity: assorted observations
Updated 12-29-2008 at 12:11 AM by Marid Audran (adding category)
- One way of writing put-call parity is
C - P = PV(F - K),
where C is call price, P is put price (and put and call have identical time to expiration and strike price K), and F is the forward price of the underlying asset. An implication is that
C > P if and only if F > K.
If F = K, then C = P. Put-call parity says nothing about what C and P are equal to in this case, however; that depends on how volatile the stock is. If F = K and there's zero volatility, then you're risk-free and C = P = 0.
- Another way of writing the parity relationship is
C + PV(K) = P + PV(F).
I had read in a forum post that one of the seminars (TIA? I lost the reference--sorry) expressed it this way and that it made more sense to the poster (but they didn't elaborate). I thought about it, and here's one way to make sense of it: If X is the spot price at expiration, then
both sides of that equation have a payoff of max(X,K).
On the one hand, if you buy a call option and lend out the present value of K, then upon expiration you get back K and (if X>K) an additional X-K.
On the other hand, if you buy a put and enter into a prepaid forward contract (the cost of the latter is PV(F)), then upon expiration you can sell the asset with a guaranteed price of K (thanks to the put).
- Found a job outside the industry (04-29-2009)
- If A,B,C are independent, then AnB (resp., AuB) and C are independent (02-02-2009)
- Probability theory textbook: Secret weapon or red herring? (02-01-2009)
- Note to self: Read "Qualifications" list in job postings from the bottom upward (01-28-2009)
- Divergence of the harmonic series, in a probability context (01-27-2009)