Cheapest to Deliver (CTD): Definition and Calculation Formula

The cheapest-to-deliver (CTD) bond is the bond in a futures contract that has the lowest cost to deliver to the buyer at expiration. The CTD bond is determined by calculating the net cost of delivering each bond in the contract and then selecting the bond with the lowest net cost. The net cost of delivering a bond is the difference between the bond's price and its accrued interest.

The CTD bond is important because it determines the price of the futures contract. The futures price is equal to the price of the CTD bond plus the cost of carry, which is the interest that would be earned on the bond if it were held to maturity.

The CTD bond can change over time as the prices of the bonds in the contract change. If the price of one bond in the contract rises relative to the others, it will become the CTD bond. This is because the higher-priced bond will have a higher net cost of delivery, and therefore a higher futures price.

The CTD bond is used to calculate the daily settlement price of the futures contract. The settlement price is the price at which the futures contract is marked to market at the end of each trading day. The settlement price is equal to the price of the CTD bond plus the cost of carry.

The CTD bond is also used to calculate the margin requirement for the futures contract. The margin requirement is the amount of money that a trader must deposit with their broker in order to hold a futures position. The margin requirement is based on the price of the CTD bond and the cost of carry.

The CTD bond is an important concept in futures trading. It is used to determine the price of the futures contract, the daily settlement price, and the margin requirement. By understanding the CTD bond, traders can better understand how futures contracts work and make more informed trading decisions.

Here is a more mathematical explanation of the CTD bond calculation:

The CTD bond is the bond in a futures contract that has the lowest net cost to deliver to the buyer at expiration. The net cost of delivering a bond is the difference between the bond's price and its accrued interest.

The CTD bond is calculated by finding the bond in the contract with the lowest price plus accrued interest. The price of a bond is the present value of its cash flows, and the accrued interest is the interest that has accumulated on the bond since the last coupon payment.

The price of a bond is calculated using the following formula:

Price = PV(Coupon Payments) + PV(Maturity Value)

where:

PV(Coupon Payments) is the present value of the bond's coupon payments

PV(Maturity Value) is the present value of the bond's maturity value

The accrued interest is calculated using the following formula:

Accrued Interest = (Bond Price - Par Value) * (Days to Coupon / 360)

where:

Bond Price is the price of the bond

Par Value is the face value of the bond

Days to Coupon is the number of days until the next coupon payment

360 is the number of days in a year

Once the price and accrued interest of each bond in the contract have been calculated, the CTD bond is the bond with the lowest price plus accrued interest.

The CTD bond is important because it determines the price of the futures contract. The futures price is equal to the price of the CTD bond plus the cost of carry, which is the interest that would be earned on the bond if it were held to maturity.

The CTD bond can change over time as the prices of the bonds in the contract change. If the price of one bond in the contract rises relative to the others, it will become the CTD bond. This is because the higher-priced bond will have a higher net cost of delivery, and therefore a higher futures price.