disc2rate

Interest rates from cash flow discounting factors

Description

example

Rates = disc2rate(Compounding,Disc,EndTimes,StartTimes) computes interest rates from discount factors where interval points are input as times in periodic units.

disc2rate computes the yields over a series of NPOINTS time intervals given the cash flow discounts over those intervals. NCURVES different rate curves can be translated at once if they have the same time structure. The time intervals can represent a zero or a forward curve.

The output Rates is an NPOINTS-by-NCURVES column vector of yields in decimal form over the NPOINTS time intervals.

example

[Rates,EndTimes,StartTimes] = disc2rate(Compounding,Disc,EndTimes,StartTimes,ValuationDate,Basis,EndMonthRule) computes interest rates from discount factors where ValuationDate is passed and interval points are input as dates.

You can specify the investment intervals either with input times or with input dates. Entering ValuationDate invokes the date interpretation; omitting ValuationDate invokes the default time interpretations.

Examples

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This example shows the two uses of disc2rate.

Interval Points Are Input as Times in Periodic Units

Compute rates from a zero curve at 6 months, 12 months, and 24 months, given the discount factors for these periods. The times to the cash flows are 1, 2, and 4. disc2rate assumes that the valuation date corresponds to time = 0.

Compounding = 2;
Disc = [0.9756; 0.9426; 0.8799];
EndTimes   = [1; 2; 4];
Rates = disc2rate(Compounding, Disc, EndTimes)
Rates = 3×1

0.0500
0.0600
0.0650

Interval Points Are Input as Dates

Compute rates from a zero curve at 6 months, 12 months, and 24 months, given the discount factors for these periods. Use dates to specify the ending time horizon.

Compounding = 2;
Disc = [0.9756; 0.9426; 0.8799];
EndDates = ['10/15/97'; '04/15/98'; '04/15/99'];
ValuationDate = '4/15/97';
Rates = disc2rate(Compounding, Disc, EndDates, [], ValuationDate)
Rates = 3×1

0.0500
0.0600
0.0650

Input Arguments

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Compounding rate for which the input zero rates are compounded when annualized, specified as one of the following scalar integers. Compounding determines the formula for the discount factors (Disc):

• If Compounding = 0 for simple interest:

• Disc = 1/(1 + Z * T), where T is time in years and simple interest assumes annual times F = 1.

• If Compounding = 1, 2, 3, 4, 6, 12:

• Disc = (1 + Z/F)^(-T), where F is the compounding frequency, Z is the zero rate, and T is the time in periodic units, for example, T = F is one year.

• If Compounding = 365:

• Disc = (1 + Z/F)^(-T), where F is the number of days in the basis year and T is a number of days elapsed computed by basis.

• If Compounding = -1:

• Disc = exp(-T*Z), where T is time in years.

Data Types: double

Discounts, specified as a number of points (NPOINTS) by number of curves (NCURVES) matrix of discounts. Disc are unit bond prices over investment intervals from StartTimes, when the cash flow is valued, to EndTimes, when the cash flow is received.

Data Types: double

End times, specified as a scalar or an NPOINTS-by-1 column vector of times in periodic units ending the interval to discount over. When EndTimes is not a date, the value for EndTimes is T computed from SIA semi-annual time factors, Tsemi, by the formula T = Tsemi/2 * F, where F is the compounding frequency. F is set to 1 for continuous compounding.

Note

When ValuationDate is not passed, EndTimes is interpreted as times. If Compounding = 365 (daily), EndTimes is measured in days.

Data Types: double | char

Start times, specified a scalar or an NPOINTS-by-1 column vector of times in periodic units starting the interval to discount over. StartDates must be earlier than EndDates. When StarTimes is not a date, the value for StartTimes is T computed from SIA semi-annual time factors, Tsemi, by the formula T = Tsemi/2 * F, where F is the compounding frequency. F is set to 1 for continuous compounding.

Note

When ValuationDate is not passed, StartTimes is interpreted as times. If Compounding = 365 (daily), StartTimes is measured in days.

Data Types: double | char

Observation date of the investment horizons entered in StartTimes and EndTimes, specified as scalar date.

Note

You can specify the investment intervals either with input times or with input dates. Entering ValuationDate invokes the date interpretation; omitting ValuationDate invokes the default time interpretations.

Data Types: double | char

Day-count basis of the instrument when using dates for StartTimes and EndTimes, specified as a scalar or an NINST-by-1 vector of integers..

• 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

Data Types: double

End-of-month rule flag when using dates for StartTimes and EndTimes, specified as a scalar or an NINST-by-1 vector of nonnegative integers. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.

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

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

Data Types: double

Output Arguments

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Rates, returned as an NPOINTS-by-NCURVES column vector of in decimal form over NPOINTS time intervals.

Times ending the interval to discount over, returned as an NPOINTS-by-1 column vector, measured in periodic units.

Times starting the interval to discount over, returned as an NPOINTS-by-1 column vector, measured in periodic units.

Introduced before R2006a