bndfutprice

Price bond future given repo rates

Syntax

[FutPrice,AccrInt] = bndfutprice(RepoRatePrice,FutSettle,Delivery,ConvFactor,CouponRate,Maturity)

[FutPrice,AccrInt] = bndfutprice(___,Name,Value)

Description

[FutPrice,AccrInt] = bndfutprice(RepoRatePrice,FutSettle,Delivery,ConvFactor,CouponRate,Maturity) computes the price of a bond futures contract for one or more bonds given a repo rate, and bond properties, including the bond conversion factor. The default behavior is that the coupon reinvestment rate matches the repo rate. However, you can specify a separate reinvestment rate using optional arguments.

[FutPrice,AccrInt] = bndfutprice(___,Name,Value) specifies options using one or more optional name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

Compute the Price For a Bond Future

This example shows how to compute the price for a bond future using the following data.

bndfutprice(.064, 129, datetime(2000,9,21),datetime(2000,12,29), 1.3136, .0875, datetime(2020,8,15))

ans = 
98.1516

Input Arguments

RepoRate — Repo rates

vector

Repo rates, specified as an numBonds-by-1 vector in decimals.

Data Types: double

Price — Bond prices

vector

Bond prices, specified as an numBonds-by-1 vector in decimals.

Data Types: double

FutSettle — Future settlement date

datetime array | string array | date character vector

Future settlement date, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

Delivery — Future delivery dates

datetime array | string array | date character vector

Future delivery dates, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

ConvFactor — Bond conversion factors

vector

Bond conversion factors, specified as an numBonds-by-1 vector. For more information, see convfactor.

Data Types: double

CouponRate — Coupon rates

vector

Coupon rates, specified as an numBonds-by-1 vector of numeric decimals.

Data Types: double

Maturity — Maturity dates

datetime array | string array | date character vector

Maturity dates, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [FutPrice,AccrInt] = bndfutprice(RepoRate,Price,FutSettle,Delivery,ConvFactor,CouponRate,Maturity,'Basis',5,'Face',1000,'Period',4)

Basis — Day count basis

0 (actual/actual) (default) | integer from 0 to 13

Day count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar integer from 0 to 13.

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

EndMonthRule — End-of-month rule flag for generating floorlet dates

1 (in effect) (default) | scalar of nonnegative integer [0,1]

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar with a nonnegative integer [0, 1].

• 0 = Ignore rule, meaning that a payment date is always the same numerical day of the month.

• 1 = Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

IssueDate — Bond issue date

if you do not specify an IssueDate, the cash flow payment dates are determined from other inputs (default) | datetime scalar | string scalar | date character vector

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar datetime, string, or date character vector.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

Face — Face value of the bond

100 (default) | scalar numeric

Face value of the bond, specified as the comma-separated pair consisting of 'Face' and a scalar numeric. Face has no impact on key rate duration.

Data Types: double

FirstCouponDate — Irregular first coupon date

if you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs (default) | datetime scalar | string scalar | date character vector

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar datetime, string, or date character vector.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

LastCouponDate — Irregular last coupon date

datetime scalar | string scalar | date character vector

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar datetime, string, or date character vector.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date.

Period — Coupons per year

2 per year (default) | vector

Coupons per year, specified as the comma-separated pair consisting of 'Period' and a scalar integer. Values for Period are 0, 1, 2, 3, 4, 6, and 12.

Data Types: double

ReinvestBasis — Day count basis for reinvestment rate

identical to RepoBasis (default) | integer from 0 to 13

Day count basis for the reinvestment rate, specified as the comma-separated pair consisting of 'ReinvestBasis' and a scalar integer from 0 to 13.

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

ReinvestRate — Underlying bond annual coupon

scalar decimal numeric

Underlying bond annual coupon, specified as the comma-separated pair consisting of 'ReinvestRate' and a scalar decimal numeric.

Data Types: double

RepoBasis — Day count basis for repo rate

2 (actual/360) (default) | integer from 0 to 13

Day count basis for repo rate, specified as the comma-separated pair consisting of 'RepoBasis' and a scalar integer from 0 to 13.

• 0 = actual/actual

• 1 = 30/360 (SIA)

• 2 = actual/360

• 3 = actual/365

• 4 = 30/360 (PSA)

• 5 = 30/360 (ISDA)

• 6 = 30/360 (European)

• 7 = actual/365 (Japanese)

• 8 = actual/actual (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

StartDate — Forward starting date of payments

Settle date (default) | datetime scalar | string scalar | date character vector

Forward starting date of payments (the date from which a bond cash flow is considered), specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, string, or date character vector.

To support existing code, bndfutprice also accepts serial date numbers as inputs, but they are not recommended.

Output Arguments

FutPrice — Quoted futures price, per $100 notional

vector

Quoted futures price, per $100 notional, returned as numBonds-by-1 vector.

AccrInt — Accrued interest due at delivery date, per $100 notional

vector

Accrued interest due at delivery date, per $100 notional, returned as numBonds-by-1 vector.

More About

Repo Rate

The repo rate (also know as repurchase agreement rate) is the interest rate at which a central bank lends money to commercial banks, typically against government securities.

The repo rate is a key tool used by central banks to manage liquidity and control monetary policy. The repo rate is crucial for influencing the economy, as it directly affects borrowing costs for banks and, consequently, the interest rates available to consumers and businesses.

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.

Version History

Introduced in R2009b

R2022b: Serial date numbers not recommended

Although bndfutprice supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.