# floorbylg2f

Price floor using Linear Gaussian two-factor model

## Description

example

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.

## Examples

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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]';

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
⋮

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]';

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

Data Types: struct

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

Data Types: double

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

Data Types: double

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

Data Types: double

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

Data Types: double

Scalar correlation of the factors, specified as a scalar.

Data Types: double

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

Data Types: double

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)

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

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

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

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### 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:

$\mathrm{max}\left(FloorRate-CurrentRate,0\right)$

## Algorithms

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

$r\left(t\right)=x\left(t\right)+y\left(t\right)+\varphi \left(t\right)$

$dx\left(t\right)=-a\left(x\right)\left(t\right)dt+\sigma \left(d{W}_{1}\left(t\right),x\left(0\right)=0$

$dy\left(t\right)=-b\left(y\right)\left(t\right)dt+\eta \left(d{W}_{2}\left(t\right),y\left(0\right)=0$

where $d{W}_{1}\left(t\right)d{W}_{2}\left(t\right)=\rho dt$ 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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