Friday, September 19, 2008

Time to review the Put-Call Parity Theorem









-S = -B + P - C



Bob Murphy said...

Can you talk us through what happens when a bunch of people buy puts, rather than shorting? How does that end up pushing the share price down? Does it set up pure profit opportunities for the current owners of the shares (when put-call parity is briefly violated by the massive buying of puts)?

Bob Murphy said...

Another point: If the ban on shorting really is pointless (except maybe for raising transaction costs), then why is Wall Street apparently so happy? Is Wall St. reacting to other news and not the specific restrictions on shorting?

Vilhelm S said...

I think the ban works out anyway. For you to be able to buy the put, someone else (usually a big investment bank) has to write it. If they do, they now stand to lose from the underlying stock going down, so they will need to delta-hedge by shorting the stock. Except that they can't because that's banned. Ergo, they will refuse to write the put in the first place (or at least price it much higher than it would be in a black-scholes world where delta-hedging is possible).

Silas Barta said...

Alright, ya'll win. This is above my pay grade. But I'll do my best.

-Puts lower the stock price the same way they always do.

-No, it doesn't set up pure profit opportunities, unless there's an asymmetric ability to see the implications for stock prices.

-The rally was probably because it signaled the government's willingness to help Wall Street. (Remember, I don't claim that it has no impact, just that it can't fundamentally eliminate the ability of non-holders to bet against a stock unless they do a lot more regulation.)

-If everyone delta-hedges everything, does no one ever actually take the risk of any price movements? Surely there have to be people that write puts without completely canceling the risk. It's not like there's an infinite regress going on.

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