The fact that these delivery options are available only to the short seller of futures contracts means that collectively they provide that seller with a series of valuable put options over the underlying bonds or notes. It is therefore instructive to delve more deeply into the nature of these options and their influence on bond futures valuation.

The existence of these options depends upon the futures contract specifications. Examples of the options that can be identified are as follows.

1. The short seller’s option to choose the bonds that will be delivered under the futures contract; this is the so-called ‘quality option‘.
2. The short seller’s option to choose the day of delivery within the delivery month: one form of the so-called ‘timing options‘.
3. In the case of US Treasury bond and Treasury note futures, the option of the short seller to give notice of delivery after the futures market has closed at 2 p.m. but before 8 p.m. on each delivery day of the delivery month. Thus the short seller is able to take advantage of any suitable weakening of bond prices between 2 p.m. and 8 p.m., but to deliver at the futures settlement price set at 2 p.m. This is also a timing option but is referred to as the ‘wild card option‘.
4. Again, in the case of the US Treasury bond and Treasury note futures, the option of the short seller to choose the bond to deliver, after the last futures trading day of the delivery month and before the last day for notice of delivery which is seven trading days later. Thus the short seller can benefit from any appropriate weakening of bond prices during this seven-day period. This option is also a timing option and is known as the ‘end of month option‘.

By way of illustration of the existence of these options, the US Treasury note and Treasury bond futures contracts embody all four types of option. The long gilt future traded on LIFFE only exhibits options 1 and 2, and the Bund, the JGB and Italian government bond futures contracts only exhibit option 1. This diversity of options embedded in futures contracts highlights the need to be familiar with the contract specification before applying pricing models.

Option to choose the bond to be delivered: the quality option

On delivery day, the short has the choice of which of the deliverable bonds to deliver. If the market exhibits a flat yield curve with a yield equal to that of the notional bond, the notional bond would be valued at par and the conversion factor will equal the ratio of the market value of the bond being delivered to that of the notional bond.

However, if the market yield is not equal to that of the notional bond, or if the yield curve is not flat, then the ratio of the price of a deliverable bond to the price of the notional bond will not be perfectly accurately represented by the conversion factor. Consequently, the delivery of different bonds will result in different returns on the futures contract.

If the yield curve is flat, and yields are above the yield on the notional bond, the bond with the longest duration should be delivered because it will have suffered the largest fall in prices as yields rise. In contrast, if yields are below the yield on the notional bond, the bond with the lowest duration will be delivered because they will have risen least in price as yields fall.

However, the yield curve is never entirely flat and frequently not so even along the sector covered by the deliverable bonds. Therefore the choice is more complicated because of two factors:

1. Duration is not an accurate estimate of interest rate elasticity of the bond price when the yield curve is not flat, or when the shifts in the yield curve are not parallel.

2. The differing tax treatment of income and capital gain imparts a downward bias in the price of high coupon bonds. Thus it may be optimal to deliver cheap high coupon bonds rather than higher duration low coupon bonds when market yields are above the coupon on the notional bond.

These factors create uncertainty as to what bond will be the cheapest at delivery; thus the ability of the short side to choose which bond to deliver is a valuable option.

The option to choose the bond to deliver is more valuable the greater the relative volatility of bond prices because the greater will be the uncertainty as to which bond will be cheapest to deliver. In addition, the longer the time to delivery, the greater will be that uncertainty. Also, volatile bond prices will increase the probability of the market yield being different to that of the notional bond.

The value of the delivery option is greatest at those levels of yields where the cheapest to deliver changes. That is where changes in the yield curve cause a different bond to offer the greatest return to the cash and carry arbitrage. Thus the value of the option to choose the bond to be delivered will be greater:

• the greater the relative volatility of yield spreads between delivery grade bonds;
• the longer the time to maturity;
• the greater the volatility of bond prices generally.

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