Documentation

hjmtimespec

Specify time structure for Heath-Jarrow-Morton interest-rate tree

Description

example

TimeSpec = hjmtimespec(ValuationDate,Maturity) sets the number of levels and node times for a hjmtree and determines the mapping between dates and time for rate quoting.

example

TimeSpec = hjmtimespec(___,Compounding) adds the optional argument Compounding.

Examples

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This example shows how to specify an eight-period tree with semiannual nodes (every six months) and use exponential compounding to report rates.

Compounding = -1;
ValuationDate = '15-Jan-1999';
Maturity = datemnth(ValuationDate, 6*(1:8)');
TimeSpec = hjmtimespec(ValuationDate, Maturity, Compounding)
TimeSpec = struct with fields:
FinObj: 'HJMTimeSpec'
ValuationDate: 730135
Maturity: [8x1 double]
Compounding: -1
Basis: 0
EndMonthRule: 1

Input Arguments

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Pricing date and first observation in the tree, specified as a scalar date using a serial date number or date character vector.

Data Types: double | char

Dates marking the cash flow dates of the tree, specified as NLEVELS-by-1 vector of serial date numbers or date character vectors. Cash flows with these maturities fall on tree nodes. Maturity should be in increasing order.

Data Types: double | char | cell

(Optional) Rate at which the input zero rates were compounded when annualized, specified as a scalar integer value.

• 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

Output Arguments

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Specification for the time layout for hjmtree, returned as a structure. The state observation dates are [ValuationDate; Maturity(1:end-1)]. Because a forward rate is stored at the last observation, the tree can value cash flows out to Maturity(end).