Derivatives 101: 2

Approaching the previously described agreement in 100% mercenary terms, it should be clear that the payoff for either side depends rather closely on the relative outlays for admission and munchies. It is this dependency that makes the deal a derivative: whatever value it has derives from the value of those other things. (What their value depends on in turn is, alas, outside our bailiwick. It would be quite wrong, for example, to speculate that the presence of Christian Bale and Hugh Jackman in the movie's cast would have any effect on consumer demand.)

The things on which our contract's value depends are referred to as the underlying. In this case we have two, which at first glance might seem excessive: the majority of common derivatives are usually considered to have only one. That, however, presupposes a shared medium of exchange or metric of value, a numeraire; usually cash. While we can easily devise a contract transacted in only a single asset, it won't be a derivative; it'll either be a bond -- "I'll give you a chocolate coated marzipan rodent today, you give me two such in a month's time" -- or theft.

The simplest kind of real derivative -- where "real" here denotes existence in an abstruse financial domain having only the most notional connection to reality as it is commonly understood -- is called a forward contract: an undertaking to participate in a single fully-specified transaction at a fully-specified time in the future. This is a more or less atomic idea, and a lot of other derivatives can be conveniently conceptualised as combinations thereof.

Our own picture palace outing, for example, could be represented as a swap -- essentially an exchange of forwards (one or more on each side) -- whereby (in this case) you agree in advance to pay the going rate for popcorn and give some to me, while I agree to pay the going rate for tickets and give one to you. Neither side really fits the proper definition of a forward, though, because we don't agree the terms in advance in an external numeraire. It's more correct, and also more instructive, to consider the whole event as just a single forward denominated in one or other asset. That is:

(Note that I've quietly discarded one of the sources of uncertainty in the original discussion, to wit: how much popcorn can I eat? But, frankly, just one large bucket would tax the digestion of even the most gluttonous moviegoer, and having the details pinned down makes the excursion a lot easier to contemplate.)

There are some issues with this model -- movie tickets are not perfectly fungible, for example: you may demand seats with a particular sightline, and what happens if they're sold out? -- but for our purposes it should suffice.

There remains, of course, the inescapable possibility that one of us will renege on our side of the bargain -- probably citing some manner of domestic distress, "My boyfriend is feeling neglected and insists that I spend the evening with him" or whatever, and how fucking annoying is that? -- leaving the other party forlorn at the theatre clutching his contribution in puffed maize or rights of admission. This possibility is called credit risk, and it plays a significant part in the structure and valuation of any security, whether derived or not, but in a way that can often be discreetly brushed under the carpet of market forces; which is to say: you would have taken it into account when you agreed the price in the first place.

Or, in other words: caveat emptor.
Posted by matt at January 20, 2006 11:33 PM