rangefloatbybdt

Price range floating note using Black-Derman-Toy tree

Syntax

[Price,PriceTree] = rangefloatbybdt(BDTTree,Spread,Settle,Maturity,RateSched)

[Price,PriceTree] = rangefloatbybdt(___,Name,Value)

Description

[Price,PriceTree] = rangefloatbybdt(BDTTree,Spread,Settle,Maturity,RateSched) prices range floating note using a Black-Derman-Toy 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.

[Price,PriceTree] = rangefloatbybdt(___,Name,Value) adds optional name-value pair arguments.

Examples

Compute the Price of a Range Note Using a Black-Derman-Toy Tree

This example shows how to compute the price of a range note using a Black-Derman-Toy tree with the following interest-rate term structure data.

Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = datetime(2011,1,1);
StartDates = ValuationDate;
EndDates = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1) ; datetime(2015,1,1)];
Compounding = 1;

% define RateSpec
RS = 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 = datetime(2011,1,1);
Maturity = datetime(2014,1,1);
RateSched(1).Dates = [datetime(2012,1,1) ; datetime(2013,1,1) ; datetime(2014,1,1)];
RateSched(1).Rates = [0.045 0.055 ; 0.0525  0.0675; 0.06 0.08];

% data to build the tree is as follows:
% assume the volatility is 10%.
Sigma = 0.1;  
BDTTS = bdttimespec(ValuationDate, EndDates, Compounding);
BDTVS = bdtvolspec(ValuationDate, EndDates, Sigma*ones(1, length(EndDates))');
BDTT = bdttree(BDTVS, RS, BDTTS);

% price the instrument 
Price = rangefloatbybdt(BDTT, Spread, Settle, Maturity, RateSched)

Price = 97.5267

Input Arguments

BDTTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using bdttree.

Data Types: struct

Spread — Number of basis points over reference rate

numeric

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

Data Types: double

Settle — Settlement date for floating range note

datetime array | string array | date character vector

Settlement date for the floating range note, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors. The Settle date for every range floating instrument is set to the ValuationDate of the BDT tree. The floating range note argument Settle is ignored.

To support existing code, rangefloatbybdt also accepts serial date numbers as inputs, but they are not recommended.

Maturity — Maturity date for floating range note

datetime array | string array | date character vector

Maturity date for the floating-rate note, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, rangefloatbybdt also accepts serial date numbers as inputs, but they are not recommended.

RateSched — Range of rates within which cash flows are nonzero

structure

Range of rates within which cash flows are nonzero, specified as a NINST-by-1 vector of structures. 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).

Data Types: struct

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is 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 enclose Name in quotes.

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

Reset — Frequency payment per year

1 (default) | numeric

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

Data Types: double

Basis — Day-count basis of instrument

0 (actual/actual) (default) | integer from 0 to 13

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

Data Types: double

Principal — Notional principal amount

100 (default) | numeric

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

Data Types: double

Options — Derivatives pricing options structure

structure

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

Data Types: struct

EndMonthRule — End-of-month rule flag for generating caplet dates

1 (in effect) (default) | nonnegative integer with value 0 or 1

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a nonnegative integer with a value of 0 or 1 using a NINST-by-1 vector.

• 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

Price — Expected prices of range floating notes at time 0

vector

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

PriceTree — Tree structure of instrument prices

structure

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.PTree contains the clean prices.

• PriceTree.AITree contains the accrued interest.

• PriceTree.tObs contains the observation times.

More About

Range Note

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 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, see Range 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

R2022b: Serial date numbers not recommended

Although rangefloatbybdt supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.