# convfactor

Bond conversion factors

## Description

example

CF = convfactor(RefDate,Maturity,CouponRate) computes a conversion factor for a bond futures contract.

example

CF = convfactor(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

## Examples

collapse all

This example shows how to calculate CF, given the following RefDate, Maturity, and CouponRate.

RefDate  = {'1-Dec-2002';
'1-Mar-2003';
'1-Jun-2003';
'1-Sep-2003';
'1-Dec-2003';
'1-Sep-2003';
'1-Dec-2002';
'1-Jun-2003'};

Maturity = {'15-Nov-2012';
'15-Aug-2012';
'15-Feb-2012';
'15-Feb-2011';
'15-Aug-2011';
'15-Aug-2010';
'15-Aug-2009';
'15-Feb-2010'};

CouponRate = [0.04; 0.04375; 0.04875; 0.05; 0.05; 0.0575; 0.06; 0.065];

CF = convfactor(RefDate, Maturity, CouponRate)
CF = 8×1

0.8539
0.8858
0.9259
0.9418
0.9403
0.9862
1.0000
1.0266

This example shows how to calculate cf, given the following RefDate, Maturity, and CouponRate for a German bond.

cf = convfactor('3/10/2009','1/04/2018', .04,.06,3)
cf = 0.8659

## Input Arguments

collapse all

Reference dates for which conversion factor is computed (usually the first day of delivery months), specified as an N-by-1 vector of serial date numbers.

Data Types: double

Maturity date, specified as a N-by-1 vector of serial date numbers.

Data Types: double

Annual coupon rates for underlying bond, specified as an numBonds-by-1 vector in decimals.

Data Types: double

### Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: CF = convfactor(RefDate,Maturity,CouponRate,'Convention',2)

Conversion factor convention, specified as the comma-separated pair consisting of 'Convention' and a N-by-1 vector using the following values:

• 1 = US Treasury bond (30-year) and Treasury note (10-year) futures contract

• 2 = US 2-year and 5-year Treasury note futures contract

• 3 = German Bobl, Bund, Buxl, and Schatz

• 4 = UK gilts

• 5 = Japanese Government Bonds (JGBs)

Data Types: double

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a N-by-1 vector using a serial date numbers.

Data Types: double

Reference semiannual yield, specified as the comma-separated pair consisting of 'RefYield' and an N-by-1 vector in decimals.

Data Types: double

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a N-by-1 vector using serial date numbers.

Data Types: double

## Output Arguments

collapse all

Conversion factors against the 6% yield par-bond, returned as an N-by-1 vector.

collapse all

### Conversion Factors

Conversion factors of US Treasury bonds and other government bonds are based on a bond yielding 6%.

Optionally, you can specify other types of bonds and yields using inputs for RefYield and Convention. For US Treasury bonds, verify the output of convfactor by comparing the output against the quotations provided by the Chicago Board of Trade (https://www.cmegroup.com/company/cbot.html).

For German bonds, verify the output of convfactor by comparing the output against the quotations provided by Eurex (https://www.eurexchange.com).

For UK Gilts, verify the output of convfactor by comparing the output against the quotations provided by Euronext (https://www.euronext.com).

For Japanese Government Bonds, verify the output of convfactor by comparing the output against the quotations provided by the Tokyo Stock Exchange (https://www.jpx.co.jp/english/).

## References

[1] Burghardt, G., T. Belton, M. Lane, and J. Papa. The Treasury Bond Basis. McGraw-Hill, 2005.

[2] Krgin, Dragomir. Handbook of Global Fixed Income Calculations. John Wiley & Sons, 2002.