rangefloatbyhw - Price range floating note using Hull-White tree

Syntax

Description

Price = rangefloatbyhw(HWTree,Spread,Settle,Maturity, RateSched) calculates the price of the range note instrument at the valuation date using an HW model.

[Price,PriceTree] = rangefloatbyhw(HWTree,Spread,Settle, Maturity,RateSched,Name,Value) calculates the price of the range note instrument at the valuation date and the price evolution for one or more range instruments using an HW model with additional options specified by one or more Name,Value pair arguments.

Input Arguments

HWTree	Interest-rate tree structure created by hwtree.
Spread	NINST-by-1 vector of the number of basis points over the reference rate.
Settle	NINST-by-1 vector of dates representing the settle date of the range floating note. Note   The Settle date for every range floating instrument is set to the ValuationDate of the HW tree. The range floating note argument Settle is ignored.
Maturity	NINST-by-1 vector of dates representing the maturity date of the floating-rate note.
RateSched	NINST-by-1 vector of structures representing the range of rates within which cash flows are nonzero. Each element of the structure array contains two fields: RateSched.Dates — NDates-by-1 cell array of dates corresponding to the range schedule. RateSched.Rates — NDates-by-2 array 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 date RateSched.Dates(n) is nonzero for rates in the range RateSched.Rates(n,1) < Rate < RateSched.Rate (n,2).

Name-Value Pair Arguments

'Basis'	NINST-by-1 vector representing the day-count basis used when annualizing the input forward rate tree. 0 = actual/actual 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (BMA) 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/actual (ISDA) 13 = BUS/252 For more information, see basis. Default: 0 (actual/actual)
'EndMonthRule'	NINST-by-1 vector for end-of-month rule. Values are 1 (in effect) and 0 (not in effect). Default: 1 (in effect)
'Options'	Structure created with derivset containing derivatives pricing options. Default: None
'Principal'	NINST-by-1 vector of the notional principal amount. Default: 100
'Reset'	NINST-by-1 vector representing the frequency of payments per year. Default: 1

Output Arguments

Price	NINST-by-1 vector for expected prices at time 0.
PriceTree	Structure containing trees of vectors of instrument prices and accrued interest, and a vector of observation times for each node. Values are: PriceTree.PTree contains the clean prices. PriceTree.AITree contains the accrued interest. PriceTree.tObs contains the observation times.

Definitions

Range Note Instrument

A range note is 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 directs exposure to the reference rate. In return for the drawback that no interest will be paid for the time the range is left, they offer higher coupon rates than comparable standard products, like vanilla floating notes.

Examples

Compute the price of a range note:

% The data for the interest rate term structure is as follows:
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;

%  Create RateSpec
RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding);
                       
% Instrument
% The range note 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];

% The data to build the tree is as follows:
VolDates = ['1-Jan-2012'; '1-Jan-2013'; '1-Jan-2014';'1-Jan-2015'];
VolCurve = 0.01;
AlphaDates = '01-01-2015';
AlphaCurve = 0.1;

HWVS = hwvolspec(RS.ValuationDate, VolDates, VolCurve,... 
AlphaDates, AlphaCurve);
HWTS = hwtimespec(RS.ValuationDate, VolDates, Compounding);
HWT = hwtree(HWVS, RS, HWTS);

%Price the instrument  
Price = rangefloatbyhw(HWT, Spread, Settle, Maturity, RateSched)

Price =

   96.6501

References

Jarrow, Robert, Modelling Fixed Income Securities and Interest Rate Options, Stanford Economics and Finance, 2nd edition, 2002.

See Also

bondbyhw | capbyhw | cfbyhw | fixedbyhw | floorbyhw | hwtree | instrangefloat | rangefloatbybdt | rangefloatbybk | rangefloatbyhjm | swapbyhw

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