Bond_Functions

Function Start Date within Bond returns the bond's start date.
It equals the first date in the accrual schedule and does not necessarily coincide with the payment date of the first coupon.

Function Dirty Price within Bond returns the bond's dirty price (based on a notional of 100) at a given settlement date T
It is defined as the present value of all cash flows received after T when the bond's notional is assumed to equal 100.
There exist 3 distinct methods for obtaining the dirty price:
1) From a given clean price.
2) From a given flat yield that acts as the discount zero rate for all cash flows.
3) From a given discounting yield curve that implies the discount factors to be used for discounting the various cash flows.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Clean Price within Bond returns the bond's clean price at a given settlement date T
It is defined as the bond's dirty price at T minus any interest amount (based on a notional of 100) that has been accrued until T during the coupon accrual period containing T
There exist 4 distinct methods for obtaining the clean price:
1) From a given dirty price.
2) From a given flat yield that acts as the discount zero rate for all cash flows.
3) From a given discounting yield curve that implies the discount factors to be used for discounting the various cash flows.
4) From a given discounting (treasury or swap rate) yield curve plus a Z-spread over that curve that combined imply the discount factors to be used for discounting the various cash flows.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Start Date within Bond returns the bond's start date.
It equals the first date in the accrual schedule and does not necessarily coincide with the payment date of the first coupon.

Function Maturity Date within Bond returns the bond's maturity date.
It equals the last date in the accrual schedule and does not necessarily coincide with the payment date of the last coupon.

Function Is Tradable within Bond returns true if there exist cash flows to be paid after the given settlement date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Previous Cash Flow Date within Bond returns the payment date of the cash flow associated with the accrual period preceding the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Next Cash Flow Date within Bond returns the payment date of the cash flow associated with the accrual period following the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Previous Cash Flow Amount within Bond returns the cash flow amount associated with the accrual period preceding the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Next Cash Flow Amount within Bond returns the cash flow amount associated with the accrual period following the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Previous Coupon Rate within Bond returns the coupon rate of the accrual period preceding the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Next Coupon Rate within Bond returns the coupon rate of the accrual period following the given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrual Start Date within Bond returns the start of the accrual period containing a given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrual End Date within Bond returns the end of the accrual period containing a given reference date T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Reference Period Start within Bond returns the start of the reference period containing a given reference date T
Note the reference period can differ from the corresponding accrual period and is needed in the calculation of the time length of the accrual period by a few day count conventions, such as ACT/ACT(ICMA)
If T is not explicitly given, it will be set to the default bond settlement date.

Function Reference Period End within Bond returns the end of the reference period containing a given reference date T
Note the reference period can differ from the corresponding accrual period and is needed in the calculation of the time length of the accrual period by a few day count conventions, such as ACT/ACT(ICMA)
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrual Period within Bond returns the bond's accrual period at a given reference date T
This equals the number of calendar days of the accrual period containing T expressed in annual units according to the bond's day count convention.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrual Days within Bond returns the bond's accrual days at a given reference date T
This equals the number of calendar days of the accrual period containing T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrued Period within Bond returns the bond's accrued period at a given reference date T
This equals the number of calendar days from the start of the accrual period containing T until T expressed in annual units according to the bond's day count convention.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrued Days within Bond returns the bond's accrued days at a given reference date T
This equals the number of calendar days from the start of the accrual period containing T until T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Accrued Amount within Bond returns the bond's 100-scaled accrued amount at a given reference date T
This equals the interest amount that has been earned up to T during the accrual period containing T assuming a notional of 100.
If T is not explicitly given, it will be set to the default bond settlement date.

Function BPS within Bond returns the basis-point sensitivity of the bond's cash flows as of a given reference date T
The result is the change in NPV (on a notional of 100) due to a uniform 1-basis-point change in the rate paid by the cash flows.
There exist 2 distinct methods for obtaining the NPV:
1) From a given flat yield that acts as the discount zero rate for all cash flows.
2) From a given discounting yield curve that implies the discount factors to be used for discounting the various cash flows.
If T is not explicitly given, it will be set to the default bond settlement date.

Function ATM Rate within Bond returns the At-The-Money rate as of a given reference date T
This is the theoretical flat coupon rate that the bond would need to have in order for its calculated clean price to equal a given clean price input.
A discounting yield curve must be provided.
If a clean price is not provided, it is calculated from the given discounting yield curve.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Duration within Bond returns the duration as of a given reference date T
The exact duration definition should be specified out of the list Bond::Duration Type
If T is not explicitly given, it will be set to the default bond settlement date.

Function KRD within Bond returns the Key Rate Duration (KRD) as of a specified array of future times T1, T2, ..., TN
KRD is defined and implemented outside of QuantLib as follows:

Let P be the bond's dirty price as of the bond's settlement date T
KRD is an array of N numbers D1, D2, ..., DN, such that Di represents the sensitivity of P upon changing the zero rate ri corresponding to maturity Ti

More specifically, Di = (P'-P'')/(2ΔP), where P' is the dirty bond price calculated using a yield curve built out of flat zero rates r1, r2, ..., rN all equal to the bond yield y except of the zero rate ri, which is shifted downwards by the amount Δ
Similarly, P'' is the dirty bond price calculated using the same yield curve, but this time with the zero rate shifted upwards by Δ

Note that both the bond's yield y and the zero rates ri are defined with Simple Rate::Compounding::Simple compounding convention.
Also the yield curve is built using linear interpolation and flat extrapolation with respect to the zero rates.
This means, shifting for example the rate r2 means that the rate r(t) for T1 < t < T2 will be shifted by the amount Δ(t-T1)/(T2-T1)
Similarly, the rate r(t) for T2 < t < T3 will be shifted by the amount Δ(T3-t)/(T3-T2)
If T is not explicitly given, it will be set to the default bond settlement date.

Function Convexity within Bond returns the convexity as of a given reference date T
The convexity is defined as follows:
Let y be an assumed given yield (flat yield to maturity) for our bond.
Let P be the bond's dirty price as of T
Then the second derivative (a measure of curvature) C of P with respect to y is computed.
Note that C will depend on the conventions defining the yield y
Convexity is then defined as C/P
If T is not explicitly given, it will be set to the default bond settlement date.

Function Basis Point Value within Bond - also known as DV01 - returns the basis point value as of a given reference date T
It equals the change in NPV (on a notional of 100) caused by an increase in yield by one basis point.
Obtained by setting dy = 0.0001 in the 2nd-order Taylor series expansion.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Yield Value Basis Point within Bond returns the yield value of a basis point as of a given reference date T
The yield value of a one basis point change in price is the derivative of the yield with respect to the price multiplied by 0.01
If T is not explicitly given, it will be set to the default bond settlement date.

Function Z Spread within Bond returns the Z-spread as of a given reference date T
Here the Z-spread is defined as the single rate z that when added to the time-dependent "risk-free" rate r, produces the time-dependent rate r+z, which when used to discount all future bond cash flows down to time T, the resulting present value equals the given dirty bond price at the same time T
This function requires the input of a "risk-free" curve - a treasury or swap curve - that is used to imply the time-dependent rate r
It also needs the bond clean price as of time T, so that the respective dirty price can be calculated.
If T is not explicitly given, it will be set to the default bond settlement date.

Function Yield within Bond returns the theoretical bond yield to maturity (same as internal rate of return) as of a given reference date T
Here the yield is defined as the single rate r that when used to discount all future bond cash flows down to time T, the resulting present value equals the given dirty bond price at the same time T
There exist 2 distinct methods for obtaining the yield:
1) From a given clean price as of time T, which is used to imply the needed respective dirty price.
2) From a given discounting yield curve that is used to calculate the needed dirty price at time T
If T is not explicitly given, it will be set to the default bond settlement date.

Function Settlement Value within Bond returns the bond's settlement value as a function of the clean price.
This is based on the actual bond's notional (not scaled to 100).
The theoretical settlement value is returned if no clean price is provided.
The default bond settlement date is used for calculation.