disc2rate

Interest rates from cash flow discounting factors

Syntax

Rates = disc2rate(Compounding,Disc,EndTimes,StartTimes)

[Rates,EndTimes,StartTimes] = disc2rate(Compounding,Disc,EndTimes,StartTimes,ValuationDate,Basis,EndMonthRule)

Description

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.

[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

Compute Interest Rates from Cash Flow Discounting Factors

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

Compounding — Compounding rate

integer with value of 0, 1, 2, 3, 4, 6, 12, 365, -1

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

Disc — Discounts

matrix

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

EndTimes — End times

serial date number | date character vector | numeric

End times, specified as a scalar or an NPOINTS-by-1 column vector using serial date numbers or date character vectors, or 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

StartTimes — Start times

serial date number | date character vector | numeric

Start times, specified a scalar or an NPOINTS-by-1 column vector using serial date numbers or date character vectors, or 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

ValuationDate — Observation date of the investment horizons entered in StartTimes and EndTimes

serial date number | date character vector

Observation date of the investment horizons entered in StartTimes and EndTimes, specified as scalar serial date number or date character vector.

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

Basis — Day-count basis

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

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

For more information, see Basis.

Data Types: double

EndMonthRule — End-of-month rule flag

1 (in effect) (default) | nonnegative integer with values 0 or 1

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

Rates — Rates

vector

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

EndTimes — Times ending the interval to discount over

vector

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

StartTimes — Times starting the interval to discount over

vector

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

More About

Discount Factor

A discount factor is a multiplier used to convert future cash flows into their present value.

Discount factors are derived from the interest-rate curve (often referred to as the rate curve) and are used to discount future cash flows back to their present value.

Version History

Introduced before R2006a