Treasury bond futures: Valuing the delivery options

Abstract

wning a security with a guaranteed future sale price and date is (almost) 0 equivalent to a short-term investment extending to the sale date. Yet, in the Treasury bond futures market the prices seem too low to provide a fair rate of return to those who short T-bond futures. That is, the short term interest rate implicit in a long cash T-bondshort T-bond futures position is below the rep0 rate observed in the cash markets. Over the last several years, the difference between implied short-term interest rate (usually referred to as the implied rep0 rate) and the actual rep0 rate has been on the order of 250 basis points. In explaining this, market analysts have noted that there are two peculiarities in the bond delivery process which favor the individual who has the short position and cause bond futures to trade for less than their theoretical price.The first of these peculiarities is what is often called the "wild card" or daily option on Treasury bond futures. During the delivery month the holder of a short position has until 9 p.m. (NY time) to notify the exchange of the intention to deliver.The invoice price is calculated from the futures settlement price at 3 P.m. (NY time) on the day notice is given. Since the cash market is open until 5 p.m. (NY time), or two hours more, there is a possibility of buying cheaply late in the day and selling at the pre-established price. This possibility exists for these two hours each day during the delivery month.The second delivery quirk is often called the implicit put option or "end of month" option which applies to the last seven business days of the delivery month. 'We say almost because if a coupon drop occurs during the holding period, the investment of the coupon sum does not have a guaranteed return.

Pricing the Chicago Board of Trade T-Bond futures

“…This is consistent with some empirical studies arguing that market futures prices are lower than what they should be when the term structure of interest rates is upward sloping. Arak and Goodman (1987) conclude that T-Bond futures prices are too low and therefore believe that the market overvalues the embedded delivery options. Barnhill (1980) provides empirical evidence that futures prices are more often too low than too high.…”

“…While the quality option is assumed to be the most important, ignoring the other delivery options may lead to mispricing, and fail to suggest optimal delivery strategies. A last stream of research considers the timing option, either separately Manaster 1986, Kane andMarcus 1986b), or in conjunction with the quality option (Arak and Goodman 1987, Boyle 1989, Peck and William 1990, Gay and Manaster 1991, Nielsen and Ronn 1997, Chen and Yeh 2005, Hranaoiva et al 2005, Chen et al 2009). It is worth mentioning that the papers in this last category use simplifying assumptions on the dynamics of the interest rate or on the strategies.…”

The impact of delivery options on futures prices: A survey

“…The estimates vary considerably by time period, but are generally much smaller than those of Kane and Marcus. Arak and Goodman (1987) value the wild card option using the Black and Scholes (1973) model; they also obtain much smaller values than Kane and Marcus. Hegde (1988, 1990a), LaBarge (1988), and Hemler (1990 have all studied the quality option in Treasury bond futures contracts.…”

The municipal‐treasury futures spread

“…The value of the delivery options also created a problem, as the market valuation of these options seems to be higher than studies estimate they should be (Arak and Goodman, 1987). In this study we use the market valuation of the options.…”

“…This is called the end-of-month option. The value of these options is discussed in Arak and Goodman (1987).…”