1. ABSTRACT
The purpose of this paper is to explian the theoricital idas behind Bond Future CTD in the EUR Market.

2. Table of Content INTRODUCTION – Bond Future and CTD UNDERLYING
CONVERSION FACTOR
CALCULATION OF CTD

3. INTRODUCTION
Bond futures are exchange – tradeed instruments, with an underlying , which has a basket to deliver bond.
Usually majority of the bond furture has a short party which have the option to deliver any instruments in the basket.
DEFINATION OF BOND FUTURE:
A bond future is a contact obligation for the contract holder to purchase or sell a bond on a specified date at a predetermined price. Therefore a bond future can be bought in a future exchange market , the price and dates are determined at time the future is purchase

4. UNDERLYING
Underlying can be define as follows, in a derivates, the security that must be delivered when a derivate contract is exercised.
FOR EXAMPLE
Those are one or more specific government bonds, since diffrent future on a different market have different names such as EUR BUND future,US treasury bond future, etc,
Therefore a bond future contract is a synthetic bond with a defined terms and defined coupon, with such instrument like bond put, bond call, money market security, credit default swap, Treasuries .

5. Example of Synthetic Bond
Example: The underlying of a EUR-Bund future is a synthetic bond with a 10-years with 6% Coupon.
CTD
Since the deliveries consist of a basket of underlying bonds, it is important to calculate which of the deliveries that is most cheap to deliver. This is called Cheapest-To –Deliver (CTD)
Under this heading we are going to examine the following procedure on Bond Futures:

6. CONVERSION FACTOR
This is generate by Chicago board of trade to deliver 100,000 face value of bond in the future contact, the counter party has the chose to selcet which government bound is to deliver as part of the contract, the short position that is the counter party as the choose to selcet 20 or more different government bond for delivery and each bound have a different coupon.

7. HOW IS IT POSSIBLE? IS POSSIBLE BY CONVERSION FACTOR
Conversion factor is design to put those US years 9% coupon Government bond and years 5% coupon bond on a level plain filledwith EUR market . This is done by US Treasury department to make eeasy for each deliver any bond from the basket.
The procedure is to said Cf X quoted Price= indifference to which bond the short wish to deliver at the delivery date. (THIS IS THE PURPOSE OF CONVERSION FACTOR)

8. CALCULATION OF CHEAPEST TO DELIVER
ASSUMPTION IN CALCULATION OF CTD
1. Rate (CBOT) 6%
months maturity date which means years bond will be rounddown to the next year maturity of the three months for each instrument.
To calculate the CTD:
CTD = Min[Quoted Bond price – (settlement) (CF)]
Cost of the Bond = Dirty price i.e quoted bond price + Accrued interest.

9. Bond Price CF Cost Benefit 1 $99.50 1.0382 2.69 (2.69)
Short receive= (settlement price)(CF) + Accrued Interest
CTD Example:
Bond Price CF Cost Benefit
$ (2.69)
$ (1.87)
$ (2.12)
To calculate the CTD benfit, we use the
Below formula
CTD = Max[Quoted Bond price – (settlement) (CF)]
Q.E.D