Price options on floating-rate notes for Black-Derman-Toy interest-rate tree
[
prices options on floating-rate notes from a Black-Derman-Toy interest rate tree.
Price,PriceTree]
= optfloatbybdt(BDTTree,OptSpec,Strike,ExerciseDates,AmericanOpt,Spread,Settle,Maturity)optfloatbybdt computes prices of options on vanilla floating-rate
notes.
[
adds optional name-value pair arguments. Price,PriceTree]
= optfloatbybdt(___,Name,Value)
Define the interest-rate term structure.
Rates = [0.03;0.034;0.038;0.04]; ValuationDate = 'Jan-1-2012'; StartDates = ValuationDate; EndDates = {'Jan-1-2013'; 'Jan-1-2014'; 'Jan-1-2015'; 'Jan-1-2016'}; Compounding = 1;
Create the RateSpec.
RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,... 'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [4x1 double]
Rates: [4x1 double]
EndTimes: [4x1 double]
StartTimes: [4x1 double]
EndDates: [4x1 double]
StartDates: 734869
ValuationDate: 734869
Basis: 0
EndMonthRule: 1
Build the BDT tree and assume a volatility of 10%.
Sigma = 0.1; BDTTimeSpec = bdttimespec(ValuationDate, EndDates); BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Sigma*ones(1, length(EndDates))'); BDTT = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec)
BDTT = struct with fields:
FinObj: 'BDTFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [734869 735235 735600 735965]
TFwd: {[4x1 double] [3x1 double] [2x1 double] [3]}
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]}
FwdTree: {1x4 cell}
The floater instrument has a spread of 10, a period of one year, and matures on Jan-1-2016.
Spread = 10; Settle = 'Jan-1-2012'; Maturity = 'Jan-1-2016'; Period = 1;
Define the option for the floating-rate note.
OptSpec = {'call'; 'put'};
Strike = [100;101];
ExerciseDates = 'Jan-1-2015';
AmericanOpt = 1;Compute the price of the call and put options.
Price= optfloatbybdt(BDTT, OptSpec, Strike, ExerciseDates,AmericanOpt, Spread,...
Settle, Maturity)Price = 2×1
0.3655
0.8087
BDTTree — Interest-rate tree structureInterest-rate tree specified as a structure by using bdttree.
Data Types: struct
OptSpec — Definition of option Definition of option as 'call' or 'put' specified
as a NINST-by-1 cell array of
character vectors for 'call' or 'put'.
Data Types: cell | char
Strike — Option strike price valuesOption strike price values specified nonnegative integers using
as NINST-by-NSTRIKES vector
of strike price values.
Data Types: single | double
ExerciseDates — Exercise date for option (European, Bermuda, or American) Exercise date for option (European, Bermuda, or American) specified
as serial date numbers or date character vectors using a NINST-by-NSTRIKES or NINST-by-2 vector
of for the option exercise dates.
If a European or Bermuda option, the ExerciseDates is
a 1-by-1 (European) or 1-by-NSTRIKES (Bermuda)
vector of exercise dates. For a European option, there is only one ExerciseDate on
the option expiry date.
If an American option, then ExerciseDates is
a 1-by-2 vector of exercise
date boundaries. The option exercises on any date between or including
the pair of dates on that row. If there is only one non-NaN date,
or if ExerciseDates is 1-by-1,
the option exercises between the Settle date and
the single listed ExerciseDate.
Data Types: double | char | cell
AmericanOpt — Option type[0,1]Option type specified as NINST-by-1 positive
integer scalar flags with values:
0 — European/Bermuda
1 — American
Data Types: single | double
Spread — Number of basis points over the reference rateNumber of basis points over the reference rate specified as
a vector of nonnegative integers for the number of instruments (NINST)-by-1).
Data Types: single | double
Settle — Settlement dates of floating-rate noteValuationDate of BDT Tree (default) | serial date number | vector of serial date numbers | date character vector | cell array of date character vectorsSettlement dates of floating-rate note specified as serial date numbers or date character
vectors using a NINST-by-1 vector of dates.
Note
The Settle date for every floating-rate note is set to the
ValuationDate of the BDT tree. The floating-rate note
argument Settle is ignored.
Data Types: double | cell | char
Maturity — Floating-rate note maturity dateFloating-rate note maturity date specified as serial date numbers
or date character vectors using a NINST-by-1 vector
of dates.
Data Types: double | cell | char
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
[Price,PriceTree]=optfloatbybdt(BDTTree,OptSpec,Strike,ExerciseDates,AmericanOpt,Spread,Settle,Maturity,'FloatReset',4,'Basis',7)
'FloatReset' — Frequency of payments per year1
(default) | positive integer from the set[1,2,3,4,6,12] | vector of positive integers from the set
[1,2,3,4,6,12]Frequency of payments per year, specified as the comma-separated pair consisting
of 'FloatReset' and positive integers for the values
[1,2,3,4,6,12] in a
NINST-by-1 vector.
Note
Payments on floating-rate notes (FRNs) are determined by the effective interest-rate between reset dates. If the reset period for an FRN 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 will be more than one possible path for connecting the two payment dates.
Data Types: double
'Basis' — Day-count basis of the instrument0 (actual/actual) (default) | positive integers of the set [1...13] | vector of positive integers of the set [1...13]Day-count basis of the instrument, specified as the comma-separated pair consisting of
'Basis' and a positive integer using a
NINST-by-1 vector. The
Basis value represents the 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 (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' — Principal values100 (default) | vector of nonnegative values | cell array of nonnegative valuesPrincipal values, specified as the comma-separated pair consisting of
'Principal' and nonnegative values using a
NINST-by-1 vector or
NINST-by-1 cell array of notional principal
amounts. When using a NINST-by-1 cell array,
each element is a NumDates-by-2 cell array where
the first column is dates and the second column is associated principal amount. The
date indicates the last day that the principal value is valid.
Data Types: double | cell
'Options' — Structure containing derivatives pricing optionsStructure containing derivatives pricing options, specified as the comma-separated pair
consisting of 'Options' and structure obtained from using derivset.
Data Types: struct
'EndMonthRule' — End-of-month rule flag1 (in effect) (default) | nonnegative integer [0,1]End-of-month rule flag, specified as the comma-separated pair consisting of
'EndMonthRule' and a nonnegative integer [0,
1] using a NINST-by-1
vector. This rule applies only when Maturity is an end-of-month
date for a month having 30 or fewer days.
0 = Ignore rule, meaning that a bond coupon payment date
is always the same numerical day of the month.
1 = Set rule on, meaning that a bond coupon payment date
is always the last actual day of the month.
Data Types: double
Price — Expected prices of the floating-rate note option at time 0Expected prices of the floating-rate note option at time 0 is
returned as a scalar or an NINST-by-1 vector.
PriceTree — Structure of trees containing vectors of option prices at each node Structure of trees containing vectors of instrument prices and accrued interest and a vector of observation times for each node returned as:
PriceTree.PTree contains option
prices.
PriceTree.tObs contains the observation
times.
A floating-rate note option is a put or call option on a floating-rate note.
Financial Instruments Toolbox™ supports three types of put and call options on floating-rate notes:
American option — An option that you exercise any time until its expiration date.
European option — An option that you exercise only on its expiration date.
Bermuda option — A Bermuda option resembles a hybrid of American and European options; you can only exercise it on predetermined dates, usually monthly.
For more information, see Floating-Rate Note Options.
bdttree | bondbybdt | capbybdt | cfbybdt | floatbybdt | floorbybdt | instoptfloat | swapbybdt
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