floorbylg2f

Price floor using Linear Gaussian two-factor model

Syntax

FloorPrice = floorbylg2f(ZeroCurve,a,b,sigma,eta,rho,Strike,Maturity)

FloorPrice = floorbylg2f(___,Name,Value)

Description

FloorPrice = floorbylg2f(ZeroCurve,a,b,sigma,eta,rho,Strike,Maturity) returns the floor price for a two-factor additive Gaussian interest-rate model.

Note

Alternatively, you can use the Floor object to price floor instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

FloorPrice = floorbylg2f(___,Name,Value) adds optional name-value pair arguments.

Note

Use the optional name-value pair argument, Notional, to pass a schedule to compute the price for an amortizing floor.

example

Examples

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Price a Floor Using a Linear Gaussian Two-Factor Model

Open Live Script

Define the ZeroCurve, a, b, sigma, eta, and rho parameters to compute the floor price.

Settle = datetime(2007,12,15);
 
ZeroTimes = [3/12 6/12 1 5 7 10 20 30]';
ZeroRates = [0.033 0.034 0.035 0.040 0.042 0.044 0.048 0.0475]';
CurveDates = daysadd(Settle,360*ZeroTimes,1);
 
irdc = IRDataCurve('Zero',Settle,CurveDates,ZeroRates);
 
a = .07;
b = .5;
sigma = .01;
eta = .006;
rho = -.7;
 
FloorMaturity = daysadd(Settle,360*[1:5 7 10 15 20 25 30],1);
 
Strike = [0.035 0.037 0.038 0.039 0.040 0.042 0.044 0.046 0.047 0.047 0.047]';
 
Price = floorbylg2f(irdc,a,b,sigma,eta,rho,Strike,FloorMaturity)

Price = 11×1

         0
    0.4190
    0.8485
    1.3365
    1.8671
    3.1091
    4.9807
    7.8518
    9.8297
   11.4578
      ⋮

Price an Amortizing Floor Using a Linear Gaussian Two-Factor Model

Open Live Script

Define the ZeroCurve, a, b, sigma, eta, rho, and Notional parameters for the amortizing floor.

Settle = datetime(2007,12,15);
% Define ZeroCurve
ZeroTimes = [3/12 6/12 1 5 7 10 20 30]';
ZeroRates = [0.033 0.034 0.035 0.040 0.042 0.044 0.048 0.0475]';
CurveDates = daysadd(Settle,360*ZeroTimes);

irdc = IRDataCurve('Zero',Settle,CurveDates,ZeroRates);

% Define a, b, sigma, eta, and rho
a = .07;
b = .5;
sigma = .01;
eta = .006;
rho = -.7;

% Define the amortizing floors
FloorMaturity = daysadd(Settle,360*[1:5 7 10 15 20 25 30],1);
Strike = [0.025 0.036 0.037 0.038 0.039 0.041 0.043 0.045 0.046 0.046 0.046]';
Notional = {{datetime(2012,12,15) 100;datetime(2017,12,15) 70;datetime(2022,12,15) 40;datetime(2037,12,15) 10}};

% Price the amortizing floors
Price = floorbylg2f(irdc,a,b,sigma,eta,rho,Strike,FloorMaturity,'Notional',Notional)

Price = 11×1

         0
    0.2776
    0.6630
    1.1062
    1.5938
    2.5589
    3.9582
    5.4985
    6.1113
    6.2670
      ⋮

Input Arguments

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`ZeroCurve` — Zero curve for Linear Gaussian two-factor model
structure

Zero curve for the Linear Gaussian two-factor model, specified using IRDataCurve or RateSpec.

Data Types: struct

`a` — Mean reversion for first factor for Linear Gaussian two-factor model
scalar

Mean reversion for the first factor for the Linear Gaussian two-factor model, specified as a scalar.

Data Types: double

`b` — Mean reversion for second factor for Linear Gaussian two-factor model
scalar

Mean reversion for the second factor for the Linear Gaussian two-factor model, specified as a scalar.

Data Types: double

`sigma` — Volatility for first factor for Linear Gaussian two-factor model
scalar

Volatility for the first factor for the Linear Gaussian two-factor model, specified as a scalar.

Data Types: double

`eta` — Volatility for second factor for Linear Gaussian two-factor model
scalar

Volatility for the second factor for the Linear Gaussian two-factor model, specified as a scalar.

Data Types: double

`rho` — Scalar correlation of factors
scalar

Scalar correlation of the factors, specified as a scalar.

Data Types: double

`Strike` — Floor strike price
nonnegative integer | vector of nonnegative integers

Floor strike price specified, as a nonnegative integer using a NumFloors-by-1 vector of floor strike prices.

Data Types: double

`Maturity` — Floor maturity date
datetime array | string array | date character vector

Floor maturity date, specified using a NumFloors-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, floorbylg2f also accepts serial date numbers as inputs, but they are not recommended.

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 = floorbylg2f(irdc,a,b,sigma,eta,rho,Strike,FloorMaturity,'Reset',1,'Notional',100)

`Reset` — Frequency of floor payments per year
`2` (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 floor payments per year, specified as the comma-separated pair consisting of 'Reset' and positive integers for the values [1,2,4,6,12] in a NumFloors-by-1 vector.

Data Types: double

`Notional` — Notional value of floor
`100` (default) | nonnegative integer | vector of nonnegative integers

NINST-by-1 of notional principal amounts or NINST-by-1 cell array where each element 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.

Data Types: double

Output Arguments

collapse all

`FloorPrice` — Floor price
scalar | vector

Floor price, returned as a scalar or a NumFloors-by-1 vector.

More About

collapse all

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:

$\max (F l o o r R a t e - C u r r e n t R a t e, 0)$

Algorithms

The following defines the two-factor additive Gaussian interest-rate model, given the ZeroCurve, a, b, sigma, eta, and rho parameters:

$r (t) = x (t) + y (t) + ϕ (t)$

$d x (t) = - a (x) (t) d t + σ (d W_{1} (t), x (0) = 0$

$d y (t) = - b (y) (t) d t + η (d W_{2} (t), y (0) = 0$

where $d W_{1} (t) d W_{2} (t) = ρ d t$ is a two-dimensional Brownian motion with correlation ρ and ϕ is a function chosen to match the initial zero curve.

References

[1] Brigo, D. and F. Mercurio, Interest Rate Models - Theory and Practice. Springer Finance, 2006.

Version History

Introduced in R2013a

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R2022b: Serial date numbers not recommended

Although floorbylg2f 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.

floorbylg2f

Syntax

Description

Examples

Price a Floor Using a Linear Gaussian Two-Factor Model

Price an Amortizing Floor Using a Linear Gaussian Two-Factor Model

Input Arguments

`ZeroCurve` — Zero curve for Linear Gaussian two-factor model
structure

`a` — Mean reversion for first factor for Linear Gaussian two-factor model
scalar

`b` — Mean reversion for second factor for Linear Gaussian two-factor model
scalar

`sigma` — Volatility for first factor for Linear Gaussian two-factor model
scalar

`eta` — Volatility for second factor for Linear Gaussian two-factor model
scalar

`rho` — Scalar correlation of factors
scalar

`Strike` — Floor strike price
nonnegative integer | vector of nonnegative integers

`Maturity` — Floor maturity date
datetime array | string array | date character vector

Name-Value Arguments

`Reset` — Frequency of floor payments per year
`2` (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]`

`Notional` — Notional value of floor
`100` (default) | nonnegative integer | vector of nonnegative integers

Output Arguments

`FloorPrice` — Floor price
scalar | vector

More About

Floor

Algorithms

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

floorbylg2f

Syntax

Description

Examples

Price a Floor Using a Linear Gaussian Two-Factor Model

Price an Amortizing Floor Using a Linear Gaussian Two-Factor Model

Input Arguments

ZeroCurve — Zero curve for Linear Gaussian two-factor model structure

a — Mean reversion for first factor for Linear Gaussian two-factor model scalar

b — Mean reversion for second factor for Linear Gaussian two-factor model scalar

sigma — Volatility for first factor for Linear Gaussian two-factor model scalar

eta — Volatility for second factor for Linear Gaussian two-factor model scalar

rho — Scalar correlation of factors scalar

Strike — Floor strike price nonnegative integer | vector of nonnegative integers

Maturity — Floor maturity date datetime array | string array | date character vector

Name-Value Arguments

Reset — Frequency of floor payments per year 2 (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]

Notional — Notional value of floor 100 (default) | nonnegative integer | vector of nonnegative integers

Output Arguments

FloorPrice — Floor price scalar | vector

More About

Floor

Algorithms

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

`ZeroCurve` — Zero curve for Linear Gaussian two-factor model
structure

`a` — Mean reversion for first factor for Linear Gaussian two-factor model
scalar

`b` — Mean reversion for second factor for Linear Gaussian two-factor model
scalar

`sigma` — Volatility for first factor for Linear Gaussian two-factor model
scalar

`eta` — Volatility for second factor for Linear Gaussian two-factor model
scalar

`rho` — Scalar correlation of factors
scalar

`Strike` — Floor strike price
nonnegative integer | vector of nonnegative integers

`Maturity` — Floor maturity date
datetime array | string array | date character vector

`Reset` — Frequency of floor payments per year
`2` (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]`

`Notional` — Notional value of floor
`100` (default) | nonnegative integer | vector of nonnegative integers

`FloorPrice` — Floor price
scalar | vector