floorbynormal
Price floors using Normal or Bachelier pricing model
Syntax
Description
[
prices
floors using the Normal (Bachelier) pricing model for negative rates. FloorPrice
,Floorlets
]
= floorbynormal(RateSpec
,Strike
,Settle
,Maturity
,Volatility
)floorbynormal
computes
prices of vanilla floors and amortizing floors.
[
adds optional name-value pair arguments.FloorPrice
,Floorlets
]
= floorbynormal(___,Name,Value
)
Examples
Price a Floor Using Normal Model for Negative Rates
Consider an investor who gets into a contract that floors the interest rate on a $100,000 loan at –.6% quarterly compounded for 3 months, starting on January 1, 2009. Assuming that on January 1, 2008 the zero rate is .69394% continuously compounded and the volatility is 20%, use this data to compute the floor price. First, calculate the RateSpec
, and then use floorbynormal
to compute the FloorPrice
.
ValuationDate = 'Jan-01-2008'; EndDates ='April-01-2010'; Rates = 0.0069394; Compounding = -1; Basis = 1; % calculate the RateSpec RateSpec = intenvset('ValuationDate', ValuationDate, ... 'StartDates', ValuationDate,'EndDates', EndDates, ... 'Rates', Rates,'Compounding', Compounding,'Basis', Basis); Settle = 'Jan-01-2009'; % floor starts in a year Maturity = 'April-01-2009'; Volatility = 0.20; FloorRate = -0.006; FloorReset = 4; Principal=100000; FloorPrice = floorbynormal(RateSpec, FloorRate, Settle, Maturity, Volatility,... 'Reset',FloorReset,'ValuationDate',ValuationDate,'Principal', Principal,... 'Basis', Basis)
FloorPrice = 1.8212e+03
Price a Floor Using floorbynormal
and Compare to floorbyblk
Define the RateSpec
.
Settle = datenum('20-Jan-2016'); ZeroTimes = [.5 1 2 3 4 5 7 10 20 30]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = datemnth(Settle,12*ZeroTimes); RateSpec = intenvset('StartDate',Settle,'EndDates',ZeroDates,'Rates',ZeroRates)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 2
Disc: [10x1 double]
Rates: [10x1 double]
EndTimes: [10x1 double]
StartTimes: [10x1 double]
EndDates: [10x1 double]
StartDates: 736349
ValuationDate: 736349
Basis: 0
EndMonthRule: 1
Define the floor instrument and price with floorbyblk
.
ExerciseDate = datenum('20-Jan-2026');
[~,ParSwapRate] = swapbyzero(RateSpec,[NaN 0],Settle,ExerciseDate)
ParSwapRate = 0.0216
Strike = .01; BlackVol = .3; NormalVol = BlackVol*ParSwapRate; Price = floorbyblk(RateSpec,Strike,Settle,ExerciseDate,BlackVol)
Price = 1.2297
Price the floor instrument using floorbynormal
.
Price_Normal = floorbynormal(RateSpec,Strike,Settle,ExerciseDate,NormalVol)
Price_Normal = 1.9099
Price the floor instrument using floorbynormal
for a negative strike.
Price_Normal = floorbynormal(RateSpec,-.005,Settle,ExerciseDate,NormalVol)
Price_Normal = 0.0857
Input Arguments
Strike
— Rate at which floor is exercised
decimal
Rate at which floor is exercised, specified as a NINST
-by-1
vector
of decimal values.
Data Types: double
Settle
— Settlement date for floor
serial date number | date character vector | datetime object | string object
Settlement date for the floor, specified as a NINST
-by-1
vector
of serial date numbers, date character vectors, datetime objects,
or string objects.
Data Types: double
| char
| datetime
| string
Maturity
— Maturity date for floor
serial date number | date character vector | datetime object | string object
Maturity date for the floor, specified as a NINST
-by-1
vector
of serial date numbers, date character vectors, datetime objects,
or string objects.
Data Types: double
| char
| datetime
| string
Volatility
— Normal volatilities values
numeric
Normal volatilities values, specified as a NINST
-by-1
vector
of numeric values.
For more information on the Normal model, see Work with Negative Interest Rates Using Functions.
Data Types: double
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: [FloorPrice,Floorlets] = floorbynormal(RateSpec,Strike,Settle,Maturity,Volatility,'Reset',CapReset,'Principal',100000,'Basis',7)
Reset
— Reset frequency payment per year
1
(default) | numeric
Reset frequency payment per year, specified as the comma-separated
pair consisting of 'Reset'
and a NINST
-by-1
vector.
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
or a NINST
-by-1
cell array.
Each element in the NINST
-by-1
cell
array is a NumDates
-by-2
cell
array, where the first column is dates, and the second column is the
associated principal amount. The date indicates the last day that
the principal value is valid.
Use Principal
to pass a schedule to compute
the price for an amortizing cap.
Data Types: double
| cell
Basis
— Day-count basis of instrument
0
(actual/actual) (default) | integer from 0
to 13
Day-count basis of instrument representing the basis used when
annualizing the input forward rate, specified as the comma-separated
pair consisting of 'Basis'
and a NINST
-by-1
vector
of integers. Values are:
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
ValuationDate
— Observation date of investment horizon
if ValuationDate
is not specified,
then Settle
is used (default) | serial date number | date character vector | datetime object | string object
Observation date of the investment horizon, specified as the comma-separated pair consisting
of 'ValuationDate'
and a serial date number, date character
vector, datetime object, or string array.
Data Types: double
| char
| datetime
| string
ProjectionCurve
— Rate curve used in generating future cash flows
if ProjectionCurve
is not
specified, then RateSpec
is used both for discounting
cash flows and projecting future cash flows (default) | structure
The rate curve to be used in projecting the future cash flows,
specified as the comma-separated pair consisting of 'ProjectionCurve'
and
a rate curve structure. This structure must be created using intenvset
. Use this optional input if
the forward curve is different from the discount curve.
Data Types: struct
Output Arguments
FloorPrice
— Expected price of floor
vector
Expected price of the floor, returned as a NINST
-by-1
vector.
Floorlets
— Floorlets
array
Floorlets, returned as a NINST
-by-NCF
array
of caplets, padded with NaN
s.
More About
Floor
A floor is a contract that includes a guarantee setting the minimum interest rate to be received by the holder, based on an otherwise floating interest rate.
The payoff for a floor is:
Version History
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