Financial Derivatives Toolbox

ratetimes

Change time intervals defining interest rate environment

Syntax

Usage 1: ValuationDate not passed; third through sixth arguments are interpreted as times.

• [Rates, EndTimes, StartTimes] = ratetimes(Compounding, RefRates, 
  RefEndTimes, RefStartTimes, EndTimes, StartTimes)
  

Usage 2: ValuationDate passed and interval points input as dates.

• [Rates, EndTimes, StartTimes] = ratetimes(Compounding, RefRates, 
  RefEndDates, RefStartDates, EndDates, StartDates, ValuationDate)
  

Arguments

Compounding	Scalar value representing the rate at which the input zero rates were compounded when annualized. This argument determines the formula for the discount factors: 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, e.g. T = F is one year. 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. Compounding = -1 Disc = exp(-T*Z), where T is time in years.
RefRates	NREFPTS-by-NCURVES matrix of reference rates in decimal form. RefRates are the yields over investment intervals from RefStartTimes, when the cash flow is valued, to RefEndTimes, when the cash flow is received.
RefEndTimes	NREFPTS-by-1 vector or scalar of times in periodic units ending the intervals corresponding to RefRates.
RefStartTimes	(Optional) NREFPTS-by-1 vector or scalar of times in periodic units starting the intervals corresponding to RefRates. Default = 0.
EndTimes	NPOINTS-by-1 vector or scalar of times in periodic units ending the interval to discount over.
StartTimes	(Optional) NPOINTS-by-1 vector or scalar of times in periodic units starting the interval to discount over. Default = 0.
RefEndDates	NREFPTS-by-1 vector or scalar of serial dates ending the intervals corresponding to RefRates.
RefStartDates	(Optional) NREFPTS-by-1 vector or scalar of serial dates starting the intervals corresponding to RefRates. Default = ValuationDate.
EndDates	NPOINTS-by-1 vector or scalar of serial maturity dates ending the interval to discount over.
StartDates	(Optional) NPOINTS-by-1 vector or scalar of serial dates starting the interval to discount over. Default = ValuationDate.
ValuationDate	Scalar value in serial date number form representing the observation date of the investment horizons entered in StartDates and EndDates. Required in usage 2. Omitted or passed as an empty matrix to invoke usage 1.

Description

[Rates, EndTimes, StartTimes] = ratetimes(Compounding, RefRates, RefEndTimes, RefStartTimes, EndTimes, StartTimes) and [Rates, EndTimes, StartTimes] = ratetimes(Compounding, RefRates, RefEndDates, RefStartDates, EndDates, StartDates, ValuationDate) change time intervals defining an interest rate environment.

ratetimes takes an interest rate environment defined by yields over one collection of time intervals and computes the yields over another set of time intervals. The zero rate is assumed to be piecewise linear in time.

Rates is an NPOINTS-by-NCURVES matrix of rates implied by the reference interest rate structure and sampled at new intervals.

StartTimes is an NPOINTS-by-1 column vector of times starting the new intervals where rates are desired, measured in periodic units.

EndTimes is an NPOINTS-by-1 column vector of times ending the new intervals, measured in periodic units.

If Compounding = 365 (daily), StartTimes and EndTimes are measured in days. The arguments otherwise contain values, T, computed from SIA semiannual time factors, Tsemi, by the formula T = Tsemi/2 * F, where F is the compounding frequency.

The investment intervals can be specified either with input times (Usage 1) or with input dates (Usage 2). Entering the argument ValuationDate invokes the date interpretation; omitting ValuationDate invokes the default time interpretations.

Examples

Example 1.

The reference environment is a collection of zero rates at six, 12, and 24 months. Create a collection of one year forward rates beginning at zero, six, and 12 months.

• RefRates = [0.05; 0.06; 0.065];
  RefEndTimes = [1; 2; 4];
  StartTimes = [0; 1; 2];
  EndTimes   = [2; 3; 4];
  Rates = ratetimes(2, RefRates, RefEndTimes, 0, EndTimes,... 
  StartTimes)
  
  Rates =
      0.0600
      0.0688
      0.0700
  

Example 2.

Interpolate a zero yield curve to different dates. Zero curves start at the default date of ValuationDate.

• RefRates = [0.04; 0.05; 0.052];
  RefDates = [729756; 729907; 730121];
  Dates    = [730241; 730486];
  ValuationDate   = 729391;
  Rates = ratetimes(2, RefRates, RefDates, [], Dates, [],... 
  ValuationDate)
  Rates =
      0.0520
      0.0520
  

See Also

disc2rate, rate2disc

rate2disc

swapbybdt