Rights and Obligations

An option is a financial security that gives its owner the right, but not the obligation, to buy or sell an underlying asset—anything from a share of a company to a bushel of corn—at a fixed price on some future date, known as the expiration date. Options are among the simplest examples of financial derivatives: securities that derive their value from the value of other assets.

Despite the simplicity of options, pinning down their value is in fact immensely difficult. After all, determining how much a right to do something should be worth seems like a problem of philosophy, not finance. But in 1973, Fischer Black and Myron Scholes were able to put a price on an option under certain mathematical assumptions; in doing so, they revolutionized the financial industry in theory and in practice, and won a Nobel Prize along the way.

We can think of options in a broad sense as objects that are worth something to us in certain states of the world and nothing to us in others. Imagine we owned an option to buy a Clover sandwich for $10 a month from now. If a catastrophic chickpea fritter harvest drove the price of a sandwich to $15 by the option’s expiration date, a diehard Clover fan would be willing to buy the option from you for up to $5 at that time. On the other hand, if sandwiches were being sold for less than $10 a month from now, the same option would be worthless. In no case could this option make us worse off: We exploit our right to act only when doing so is beneficial, and with no obligations, we otherwise pretend we never had the option to begin with and maintain our status quo.

The Black-Scholes equation shows that the asymmetric payoff intrinsic to options makes them more valuable when the dispersion of potential outcomes—what is known as volatility—increases. Since an option limits our worst-case scenario, we would rather face, loosely speaking, more uncertainty than less when we own one. For example, our Clover option is much more valuable when a sandwich has equal chance of being sold for $15 or $5 next month, than when a sandwich has equal chance of being sold for $11 or $9. In either case, having the option costs us nothing half the time when the sandwich is sold for less than $10, but when the sandwich is sold for more, we could save $5 instead of $1.

An option is therefore a multifaceted bet. It represents a gamble not only on the direction in which the price of an asset will move, but also the magnitude of such a move. (In contrast, purely directional bets on price movements are more elegantly expressed by simply buying or selling the asset in question). And unlike participants in options markets, who speculate on but cannot influence volatility, we sometimes face option-like payouts on real-world outcomes whose volatility we can in fact control. This is almost like cheating: Owning options when we can change the volatility of the underlying is like playing blackjack when we can pick the card that shows up next.

For instance, consider this year's presidential primary race. The reward for being chosen as a party's nominee is immense, while the difference between second place and dead-last is relatively negligible notwithstanding some extra book sales. Indeed, we can understand each candidate as owning an option on their own primary performance, where the candidate receives a huge payout for a first place finish and effectively nothing for anything less. In an unusually crowded Republican field, suggesting that Muslims should be banned from entering America is volatile rhetoric that could potentially relegate a candidate to an indistinguishable mass of failed campaigns, but could just as well galvanize voters and propel him to first place. A safer campaign strategy that guarantees a third or fourth place finish, on the other hand, is in comparison almost worthless.

Closer to home, anyone who’s won a game of Monopoly should intuitively understand that safe strategies are rarely the best strategies. For example, selling someone insurance on landing on your hotel-laden properties, in exchange for fixed cash payments every turn, is likely a terrible deal for all but the most substantial premiums. While you guarantee a steady (and potentially sizable) flow of cash even when no one lands on your property, you do so at a dear cost: by giving up the possibility of an outright win from eliminating a player and accumulating an insurmountable cash lead against the others. The asymmetric payoff of Monopoly (jeers and shame for anything less than first, if you’re playing it right) creates another scenario in which volatile strategies dominate safe but otherwise similar ones.

Of course, it is true that even in winner-take-all competitions, considerations other than winning can arise. For example, it might be considered a loss of face to finish dead-last in a presidential primary race or embarrassing to be the seemingly worst Monopoly player in the room. But if our sole goal is to finish first, we should be extremely careful to distinguish safety from optimality, and take advantage of any chance we have to increase our volatility while holding all else equal.

Seeing the world in terms of options is an extraordinarily powerful viewpoint, and understanding an option as a bet on volatility is just one of many lenses with which we can examine these instruments. While even some financiers have called derivatives weapons of mass destruction, these securities per se are far from destructive: Their existence has led to the creation of fascinating theory, new ways to re-allocate risk, and yet another lens with which to think about the everyday decisions we make.

Marshall M. Zhang ’16 is a statistics and math joint-concentrator in Mather House. His column appears on alternate Thursdays.