“Eurodollar call options” (below) shows option price curves for June 2010, September 2010, September 2011 and December 2011. On this chart, the futures rates, computed as 100 minus the futures prices, are listed on the horizontal axis and the dollar premiums along the price curves are related to the corresponding rates. Premiums are higher for the larger quarterly rates because these rates are subtracted from the strike prices that are listed as 100 less the quarterly rate, and the lower the strike price the higher the call option premium.
The prices for the two short-term 2010 options are higher than the two with 2011 maturities. This pattern is predictable from the curve of eurodollar rates shown on “Eurodollar rates and yields.” As the rate curve increases with longer maturities, the result is lower futures prices as well as lower premiums for calls on September and December 2011. Price curves for June and September 2010 are closely related with just 90 days separating their expiration dates; however, September and December 2011 are more closely related because the dots for the December calls cover those for September at each quarterly rate.
When the eurodollar futures are related to the ratio of the futures rate (100 minus the futures price) to the “strike rate” (100 minus the strike price) for each strike price on “Call options on eurodollar futures” (below), longer-term calls are shown in their proper position as higher in time value than shorter-term options. June and September are approaching the futures rate/strike rate of 0, a possible barrier against continued upward price movement.
It is noted on “Call options on eurodollar futures” that the September 2011 premiums have slightly higher time values than the December 2011 calls. As time to expiration approaches over the next four quarters, it should be expected that the September calls will fall relative to December 2011, so that their two option price curves will be positioned similarly to those for June and September 2010 at the current time in April 2010. The shape of the U.S. Treasury yield curve also will play a part in their relative valuation because of the close adherence of eurodollar yields to the Treasury yield curve.
On the move
Interest rates are typically in motion, reflecting changes in the national and global economic environments. When rates are held in check temporarily by central bank monetary policy, they are unable to perform effectively as a pricing mechanism for current and future debt. In effect, there is a vacuum, or hole, in the pricing process that will be filled eventually when the interest rate market is able to perform its normal functions.
Currently, there are signs of unusual market manipulation, starting with historically low market rates and yields in the United States and continuing with the unusually low spread of eurodollar yields over the U.S. Treasury yield curve.
A final indication of unusual pricing concerns the five-year, or 20-quarter, eurodollar yield, which may be measured by the average between 2.83% for the March 2015 futures and 2.93% for June 2015. The average of these two yields, 2.88%, is slightly lower than the 2.91% yield on five-year T-note futures. This makes it likely that a broad span of eurodollar rates will need to increase to pull the eurodollar yield above the T-note yield at the five-year maturity. The five-year yield on U.S. Treasury’s 2.5% coupon, March 31, 2015, on the same day was 2.47%.
A guide to eurodollar futures
The prices listed for eurodollar futures -- 100 less the rate -- are large enough to swamp the usual calculation of option price curves using the LLP option pricing model. A better alternative is to use the rates that create eurodollar futures price changes.
The below table shows 15 strike rates for the September 2011 eurodollar futures call options on April 16, 2010. Strike rates are defined as 100 less the strike prices listed by Barchart.com. For example, a listed price of 98.370 results in a strike rate of 1.630. When the strike rates increase, the call option premiums also increase.
The table shows the call premiums predicted by the LLP option pricing model at each strike rate, with the price curve shown on “Eurodollar call options.” To compute the change in the option premium for a one-basis point change in the rate at the current market rate of 1.74%, two additional strike rates are inserted between 1.63% and 1.75%. The change in premium from 1.73% to 1.75% is $28.16, or approximately $14 per basis point.
From the premium at 1.74%, $1,308, to zero would be a change of approximately 93 basis points, which would result in an estimated range of interest rates from 0.81% to 2.67% for September 2011. Although this may be a fair prediction of potential interest rates at that forward quarter, it also would imply that eurodollar futures are related to the future -- an assumption that is appropriate when relating eurodollar quarterly rates to the forward rates implied by the U.S. Treasury yield curve.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.