# rate2disc

Discount factors from interest rates

## Description

example

Disc = rate2disc(Compounding,Rates,EndTimes,StartTimes) computes discount factors from interest rates where interval points are input as times in periodic units.

The rate2disc function computes the discounts over a series of NPOINTS time intervals given the annualized yield 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 curve or a forward curve.

The output Disc is an NPOINTS-by-NCURVES column vector of discount factors in decimal form representing the value at time StartTimes of a unit cash flow received at time EndTimes.

example

[Disc,EndTimes,StartTimes] = rate2disc(Compounding,Rates,EndTimes,StartTimes,ValuationDate,Basis,EndMonthRule) computes discount factors from interest rates 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 rate2disc.

Interval Points Are Input as Times in Periodic Units

Compute discounts from a zero curve at 6 months, 12 months, and 24 months. The times to the cash flows are 1, 2, and 4. Use rate2disc to compute the present value (at time 0) of the cash flows.

Compounding = 2;
Rates = [0.05; 0.06; 0.065];
EndTimes   = [1; 2; 4];
Disc = rate2disc(Compounding, Rates, EndTimes)
Disc = 3×1

0.9756
0.9426
0.8799

Interval Points Are Input as Dates

Compute discounts from a zero curve at 6 months, 12 months, and 24 months. Use dates to specify the ending time horizon.

Compounding = 2;
Rates = [0.05; 0.06; 0.065];
EndDates = ['10/15/97'; '04/15/98'; '04/15/99'];
ValuationDate = '4/15/97';
Disc = rate2disc(Compounding, Rates, EndDates, [], ValuationDate)
Disc = 3×1

0.9756
0.9426
0.8799

## 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

Rates, specified as a number of points (NPOINTS) by number of curves (NCURVES) matrix of rates in decimal form. Rates are the yields over investment intervals from StartTimes, when the cash flow is valued, to EndTimes, when the cash flow is received. For example, 5% is 0.05 in Rates.

Data Types: double

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

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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Discount factors, returned as an NPOINTS-by-NCURVES column vector of in decimal form representing the value at time StartTimes of a unit cash flow received at time EndTimes.

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.

## Version History

Introduced before R2006a