hjmtimespec (Financial Derivatives Toolbox)

Specify time structure for HJM interest rate tree

Syntax

TimeSpec = hjmtimespec(ValuationDate, Maturity, Compounding)

Arguments

ValuationDate
Scalar date marking the pricing date and first observation in the tree. Specify as serial date number or date string

Maturity
Number of levels (depth) of the tree. A number of levels (NLEVELS)-by-1 vector of dates marking the cash flow dates of the tree. Cash flows with these maturities fall on tree nodes. Maturity should be in increasing order.

Compounding
(Optional) Scalar value representing the rate at which the input zero rates were compounded when annualized. Default = 1. 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.

`ValuationDate`	Scalar date marking the pricing date and first observation in the tree. Specify as serial date number or date string
`Maturity`	Number of levels (depth) of the tree. A number of levels (`NLEVELS`)-by-`1` vector of dates marking the cash flow dates of the tree. Cash flows with these maturities fall on tree nodes. Maturity should be in increasing order.
`Compounding`	(Optional) Scalar value representing the rate at which the input zero rates were compounded when annualized. Default = `1`. 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.

Description

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

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

Example

Specify an eight period tree with semiannual nodes (every six months). Use exponential compounding to report rates.

Compounding = -1
ValuationDate = '15-Jan-1999'
Maturity = datemnth(ValuationDate, 6*(1:8)')
TimeSpec = hjmtimespec(ValuationDate, Maturity, Compounding)

TimeSpec = 

           FinObj: 'HJMTimeSpec'
    ValuationDate: 730135
         Maturity: [8x1 double]
      Compounding: -1
            Basis: 0
     EndMonthRule: 1

See Also

hjmtree, hjmvolspec

hjmsens hjmtree