Invoice price and accrued interest

The national debt is quoted at net price, and the net price transaction is conducted at the price excluding interest, which makes the bond quotation and accrued interest decompose, and the net price of the bond quoted in the transaction only reflects the change of the market value of the principal. In bond trading, the interest is usually calculated in days according to coupon rate, and the bondholders enjoy the interest income during the holding period, so the bonds are settled, delivered and transferred at full price. The relationship between full price and net price is as follows:

Full price = net price+accrued interest since the last interest payment date.

In fact, it is very unlikely that the deliverable bonds of 10-year treasury bond futures are exactly the same as the nominal standard bonds, and the coupon rate, remaining maturity and market price of each deliverable bond are also very different. Through the conversion factor, we can establish the relationship between spot price and futures price, and compare different kinds of deliverable bonds. We multiply the futures contract price of treasury bonds by the conversion coefficient of deliverable bonds, so as to convert the futures price into the forward price of a specific deliverable bond on the futures delivery date, which is called "adjusted futures price", namely:

Adjusted futures price = futures price × conversion coefficient

When treasury bonds futures are delivered, bears transfer delivery vouchers to bulls, who pay cash, and this cash price is the invoice price of treasury bonds futures.

Invoice price = futures price × conversion factor+accrued interest

Among them, the accrued interest is the accrued interest income of spot delivery of treasury bonds from the previous interest payment date to the corresponding payment date.

Suppose that after the expiration of the March 10-year treasury bond futures contract T 1903, the short reserve of this futures contract will be delivered with the first treasury bond in Table 3, and the coupon rate of this bond is 2.7%. The maturity date of this bond in 2026 is 1 1.3, with interest paid twice a year, and the next interest payment date is 201May 9. Suppose the futures settlement price is 96.785 yuan and the quantity is 10 lots. The conversion coefficient of national debt is 0.9796.

The last trading day of the contract is the second Friday of the delivery month, and March 8, 20 19 is the expiration date of T 1903. Assuming that short positions enter centralized delivery after the contract expires, the second trading day after the expiration is paired payment, and the interval between the last interest payment date of the spot treasury bonds and the paired payment date is 130 days, then:

100 yuan accrued interest on the delivery of treasury bonds =2.7× 130/365=0.9622 yuan.

Invoice price = (96.785× 0.9796)+0.9622 = 95.7728 (Yuan)

Each contract of treasury bond futures is a treasury bond with a face value of 6,543,800 yuan, so the invoice amount that the bulls of futures contracts need to pay to the bears is:

Invoice amount =10× (95.7728×10000) = 9577278.6 (yuan)

B

Cheapest deliverable bond

The conversion coefficient solves the problem of unified conversion of different deliverable bonds, but can't all deliverable bonds be treated equally? Actually, not yet.

In the delivery of treasury bonds futures, the seller has the right to choose, that is, as long as it is a deliverable bond stipulated by the exchange, the exchange can freely choose and the buyer can only passively accept it. If there is no difference in the value of these deliverable bonds after adjustment of conversion factors, then the question is simple. How can the seller pay for any available bonds? But in fact, when preparing for delivery, the seller will find that there is still a gap between the actual market value of these deliverable bonds and the theoretical value adjusted by the conversion factor, and sometimes the gap is not small. This will naturally lead to a question, which deliverable bond is the cheapest to choose? This is the origin of the concept of the cheapest deliverable bond (CTD bond).

The theoretical value of the bonds adjusted by the conversion coefficient is inconsistent with the actual market value, and the important reason is that the algorithm of the conversion coefficient has inherent defects. Because the calculation method of the conversion coefficient is to take all the discounted cash flow method of different bonds in their remaining term as the present value, and the discount is based on the coupon rate (3%) of nominal standard bonds, that is to say, the cash flow in the short term or after 78 years is based on 3%. This assumption is unreasonable, and it is also unreasonable to assume that the national debt yield to maturity will remain at 3% in the future. The market price of deliverable bonds usually tends to use the actual market yield to maturity to discount bonds.

The methods to find the cheapest deliverable bonds (CTD) mainly include the maximum implied repo rate method, basis method and net basis method, and the rule of thumb based on duration. If you want to know the specific ideas and algorithms of these methods in detail, you can find some relevant professional books or get them through online search.