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rangefloatbyhjm

Price range floating note using Heath-Jarrow-Morton tree

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Syntax

[Price,PriceTree] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched)
[Price,PriceTree] = rangefloatbyhjm(___Name,Value)

Description

example

[Price,PriceTree] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched)prices range floating note using a Heath-Jarrow-Morton tree.

Payments on range floating notes are determined by the effective interest-rate between reset dates. If the reset period for a range spans more than one tree level, calculating the payment becomes impossible due to the recombining nature of the tree. That is, the tree path connecting the two consecutive reset dates cannot be uniquely determined because there is more than one possible path for connecting the two payment dates.

example

[Price,PriceTree] = rangefloatbyhjm(___Name,Value)adds optional name-value pair arguments.

Examples

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Open Live Script

This example shows how to compute the price of a range note using a Heath-Jarrow-Morton tree with the following interest-rate term structure data.

Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate ='Jan-1-2011'; StartDates = ValuationDate; EndDates = {'Jan-1-2012';'Jan-1-2013';'Jan-1-2014';'Jan-1-2015'}; Compounding = 1;% define RateSpecRS = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...'EndDates', EndDates,'Rates', Rates,'Compounding', Compounding);% range note instrument matures in Jan-1-2014 and has the following RateSchedule:Spread = 100; Settle ='Jan-1-2011'; Maturity ='Jan-1-2014'; RateSched(1).Dates = {'Jan-1-2012';'Jan-1-2013';'Jan-1-2014'}; RateSched(1).Rates = [0.045 0.055 ; 0.0525 0.0675; 0.06 0.08];% data to build the tree is as follows:Volatility = [.2; .19; .18; .17]; CurveTerm = [ 1; 2; 3; 4]; MaTree = {'Jan-1-2012';'Jan-1-2013';'Jan-1-2014';'Jan-1-2015'}; HJMTS = hjmtimespec(ValuationDate, MaTree); HJMVS = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6); HJMT = hjmtree(HJMVS, RS, HJMTS);% price the instrumentPrice = rangefloatbyhjm(HJMT, Spread, Settle, Maturity, RateSched)
Price = 90.2348

Input Arguments

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Interest-rate tree structure, specified by usinghjmtree.

Data Types:struct

Number of basis points over the reference rate, specified as aNINST-by-1vector.

Data Types:double

Settlement date for the floating range note, specified as aNINST-by-1vector of serial date numbers or date character vectors. TheSettledate for every range floating instrument is set to theValuationDateof the HJM tree. The floating range note argumentSettleis ignored.

Data Types:double|char|cell

Maturity date for the floating-rate note, specified as aNINST-by-1vector of serial date numbers or date character vectors.

Data Types:double|char|cell

Range of rates within which cash flows are nonzero, specified as aNINST-by-1vector of structures. Each element of the structure array contains two fields:

  • RateSched.Dates—NDates-by-1cell array of dates corresponding to the range schedule.

  • RateSched.Rates—NDates-by-2array with the first column containing the lower bound of the range and the second column containing the upper bound of the range. Cash flow for dateRateSched.Dates(n) is nonzero for rates in the rangeRateSched.Rates(n,1) <Rate<RateSched.Rate(n,2).

Data Types:struct

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN, whereNameis the argument name andValueis the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and encloseNamein quotes.

Example:[Price,PriceTree] = rangefloatbyhjm(HJMTree,Spread,Settle,Maturity,RateSched,'Reset',4,'Basis',5,'Principal',10000)

Frequency of payments per year, specified as the comma-separated pair consisting of'Reset'and aNINST-by-1vector.

Data Types:double

Day-count basis representing the basis used when annualizing the input forward rate tree, specified as the comma-separated pair consisting of'Basis'and aNINST-by-1vector 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, seeBasis.

Data Types:double

Notional principal amount, specified as the comma-separated pair consisting of'Principal'and aNINST-by-1vector.

Data Types:double

Derivatives pricing options structure, specified as the comma-separated pair consisting of'Options'and a structure obtained from usingderivset.

Data Types:struct

End-of-month rule flag, specified as the comma-separated pair consisting of'EndMonthRule'and a nonnegative integer with a value of0or1using aNINST-by-1vector.

  • 0= Ignore rule, meaning that a payment date is always the same numerical day of the month.

  • 1= Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types:logical

Output Arguments

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Expected prices of the range floating notes at time 0, returned as aNINST-by-1vector.

Tree structure of instrument prices, returned as a structure containing trees of vectors of instrument prices and accrued interest, and a vector of observation times for each node. Values are:

  • PriceTree.PTreecontains the clean prices.

  • PriceTree.AITreecontains the accrued interest.

  • PriceTree.tObscontains the observation times.

More About

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Range Note

Arange noteis a structured (market-linked) security whose coupon rate is equal to the reference rate as long as the reference rate is within a certain range.

If the reference rate is outside of the range, the coupon rate is 0 for that period. This type of instrument entitles the holder to cash flows that depend on the level of some reference interest rate and are floored to be positive. The note holder gets direct exposure to the reference rate. In return for the drawback that no interest is paid for the time the range is left, they offer higher coupon rates than comparable standard products, like vanilla floating notes. For more information, seeRange Note.

References

[1] Jarrow, Robert. “Modelling Fixed Income Securities and Interest Rate Options.”Stanford Economics and Finance.2nd Edition. 2002.

Version History

Introduced in R2012a

See Also

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