There is nothing complex about derivatives in spite of the mystery in which they are sometimes clouded. This short piece summarises the very basics of what is a derivative and what are the components that go to make up its value.
Of Books and Jumbos
If you have ever pre-ordered anything – say a CD (showing my age) or a book (really showing my age) – you have traded in derivatives. Let’s suppose you paid £10 to order a book in advance and over the course of the next few weeks it is due to be printed, bound, delivered and to appear on those gently condescending “staff’s top picks” lists in bookshops. What is the value of the book when it is thuds onto your doormat in a month’s time? Well probably still something like £10. But what if, within moments of your pre-ordering the book, a jumbo jet falls onto the factory where the book is being printed and bound after only a handful of books have been finished and shipped? Because you pre-ordered, you are lucky enough to be delivered one of the few surviving copies and don’t have to wait the several weeks for the next run of the book. If you are an enterprising sort you might now offer the book for sale on eBay and expect it to sell for significantly more than the £10 you paid for it. So your contract to pre-order the book proved valuable. Incidentally, your contract was a derivative, specifically a “forward” or “forward purchase agreement”.
Forwards and Options
Why is this a derivative? Because its value derives from, but is not necessarily the same as, the value of the underlying (in this case the underlying is a book). Why do the values differ? To illustrate let us turn your forward purchase agreement into an option.
Imagine your local bookseller, instead of requiring you to pay £10 for the book in 4 weeks’ time, says to you, “If you come to me in 4 weeks I’ll sell you the book at £10 but you are not obliged to buy the book from me” (Your local bookseller is, of course, unlikely to give you this option for free. If anybody offers you a free option you should generally take it…). In this case you would buy the book from the bookseller in 4 weeks’ time only if the price for the book at all other booksellers were greater than £10. In other words you would exercise your option only if it were valuable for you to do so. But even prior to exercise, your option has a value. That value is made of two components: inherent value (the amount by which the market price of the book at that time exceeds the £10 price tag you and the bookseller have agreed) and time value.
Time Value
The real world is uncertain. Imagine that, just after the jumbo jet falls, but before your book is delivered to your house, global environmental vandals have torched the world’s forests (just humour me…) sending the price of paper through the roof and rendering it effectively impossible that new prints of the book can ever be run. And then the book wins some prestigious award. And then some Arthur Daley (ask your parents) character tries to get hold of as many remaining copies of the book as he can find. Each such event will increase the value of the book. We have no way of knowing whether any of them will occur but we may be able to assign some probability of their occurrence. And we can say with certainty that, over a longer period of time it is more likely that at least one of these events will occur and that the value of the book will increase. In other words, the longer the period between the date on which you buy the option from your bookseller and the date on which that option runs out, the more value there must be in that option. This is time value: a function both of the amount of time to expiry of the option and of how likely any of those price-altering events is perceived to be.
The Real World
While banks frequently deal in options and other derivatives, they rarely deal in books. But the principles are identical whether the underlying be bonds or books, shares or sugar. The value of the share (etc.) option at any time will be the sum of its inherent value (i.e. the amount by which the market price of the underlying share at that time exceeds the pre-agreed purchase price (known as the strike price) and its time value, which is a function of the likelihood of a price-altering event (which in the case of a financial asset is expressed as the volatility of that asset’s price) and the amount of time to expiry of the option.
