Do-It-Yourself Spread Options

Many institutional money managers trading equity, fixed-income or balanced portfolios against a benchmark often try to enhance yield using exotic options such as over-the-counter spread options. A hedge fund manager, for example, who believes the Italian bond market is cheap and the Spanish bond market is dear can enact that trading view by buying an OTC option on the yield spread between the two countries. Another example would be a spread option on two money market rates in the same currency. This type of instrument allows investors to take views on developments such as a steepening of the short end of the yield curve, for instance.

That OTC option, however, comes at a price. In many cases, treasurers and other end-users who track benchmarks have learned not to trust the pricing in the over-the-counter exotic market.

Smart investors who are eager to circumvent what they see as the excessively high price of OTC options can make use of a much less expensive alternative using the futures market to trade delta-type trading strategies. Users of these delta-hedged strategies with listed futures strategies must willingly forego the exact payoff of an exotic option because the value-added for that rigor—quantified in measures of gamma and vega—is less significant than yield enhancement.

They are instead turning increasingly toward the type of listed futures strategy they can implement themselves. With appropriate analytical tools (such as option pricing support, risk management systems and econometrics analysis), end-users can implement the strategy themselves.

The expense associated with using even plain-vanilla OTC spread options justifies the exercise. Usually derivatives dealers charge for exotic options premia much higher than fair value. Twenty percent over "fair value” is not unusual, meaning that a client would pay 6 percent of the underlying for an option worth 5 percent. Fair value reflects assumptions concerning volatility and correlation. If the correlation between the assets is close to one, the spread option has less value because the expected volatility of the spread is low. A dealer with an offsetting trade on the book may want to balance his position, and offer a good price toward that end. New clients might also get close to fair value on the initial trade, but they should expect to pay a premium henceforth.

Calendar trade

The following example of a listed futures calendar spread trade on the 3-month, 6-month LIBOR spread inspired by a particular investment opportunity in March 1996 is illustrative. Although U.K. economic growth was significantly below its long-term average and there was no real inflationary threat, the announcement that the United States had added more than 700,000 new jobs in February—more than double the expectations—raised inflationary fears. The implied interest rates from short-term sterling futures indicated that the market expected a U.K. base rate hike. My group, however, thought the inflationary concerns were overdone, and felt there might in fact be a politically motivated rate cut. Although this uncertainty warranted an option-type trading strategy, implied volatilities for sterling options had risen rapidly.

Enter the futures alternative. The long Dec. '96/short Sept. '96 calendar spread had fallen from zero basis points to -35 basis points at the end of March, reflecting the market's bearish view of bonds. However, that spread would return to zero if there were a rate cut. Our goal was to set up an option-type delta hedge strategy on the futures calendar spread that would reflect the bullish expectation of a narrowing spread while limiting potential losses.

A straight position of 100 calendar spreads could theoretically result in unlimited losses if the spread went infinitely negative. However, an alternative of 100 nominal spreads that could be reduced according to a delta calculation will approximately replicate the risk and payoff of an option position. Because Black-Scholes can only use positive numbers, a slight modification was introduced to account for negative spreads. Assuming the spread is struck at the money, in this case -35, the delta for a single calendar spread is computed during regular time intervals. The result, when multiplied by the notional position of 100 calendar spreads, yields the actual number of calendar spreads, between 0 and 100, that should be held to replicate the desired option-type risk and payoff.

While such delta hedging theoretically requires continuous monitoring and adjustment for changing price and volatility, the strategy yielded excellent results by holding volatility constant and using weekly adjustments. The trade, commencing on March 25, 1996, hovered around the initial spread of -35 for more than a month. The indicated delta of .50 called for a position size of 50 spreads. By mid-May, the interest rate outlook in the United Kingdom had become more optimistic. As spreads narrowed to -22 basis points, the delta on the strategy rose to .76, and with it the mandated position size swelled to 76 calendar spreads. Continued optimism on the inflation and interest rate outlook by July's end narrowed the spread to -9 basis points. With the delta greater than .95 and positions size hovering around 95, the strategy now had near full exposure to changes in the calendar spread. Narrow fluctuations in the spread continued through September 1996, and a handsome profit was realized.

The moral of the story is that the at-the-money option strategy on 100 calendar spreads futures contracts is a delta hedge for a common type of spread option: long 3mGBP/short 6M GBP. The strategy's payoff with that of the option was remarkably close over the life of the trade. Quantitatively speaking, the daily/weekly difference between the three-month and six-month implied forward rates, as tracked by the spread option, is equivalent to the daily/weekly differences in the futures calendar spread.

Empirical results bear this out. On a notional trade of 25 million pounds sterling and a strike of -21 basis points, the difference of 1 percent between the payoffs of the LIBOR rate spread option and the delta-hedging futures strategy was solely attributable to approximation error.