Negative Vega? Understanding Options on Spreads

NIKUNJ KAPADIA is with the Isenberg School of Management at the University of Massachusetts. T he recent proliferation of hedge funds has brought to the forefront the types of trading strategies that distinguish hedge funds from the more conservative mutual funds. Two major sets of trading strategies have been in the spotlight: market-neutral trades, and trades that rely on the spread between the prices of two assets. Such strategies typically make use of exotic financial instruments. To be successfully used, the value of such an exotic financial instrument must be well understood, especially as the sensitivity of its value to underlying factors may be very different from its plain-vanilla counterpart. The purpose of this article is examine the determinants of the value of one such popular financial instrument: the option on a spread. The spread option is an option on the difference in the price of two underlying assets. An example of such an option is the option on the crack spread, traded on the New York Mercantile Exchange Ž . NYMEX . The spread option can be easily used to implement trading strategies for example, a view on the volatility of the spread may be implemented by taking a position in the spread option, and making it market-neutral with appropriate positions in the underlying assets. In comparison with plain-vanilla calls and puts, the value of an option on a spread has a complicated relation with its underlying components. In particular, the relation of the value of the spread option to the volatilities of its component assets is very different from that of calls and puts to the volatility of their underlying asset. It is well known that plain-vanilla options have positive vega, where vega is the sensitivity of the option price to changes in volatility. In other words, an increase in the volatility of the underlying asset increases the value of a call or a put. The intuition underlying why the option price is a positive monotonic function of volatility is easy to understand: as the payoff on a call is truncated, an increase in volatility increases the possible gains while the magnitude of the possible loss is strictly limited and not affected by the increase in volatility. Therefore, the net effect is that the option price increases as volatility increases. However, when we consider an option on a spread, an increase in volatility of one of the assets may not increase the option value, so that the option may exhibit negative vega with respect to the volatility of one of the two assets. The specific objective of this article is to explain the relation of the value of the spread option to the volatilities of its