swaptionbylg2f

Price European swaption using Linear Gaussian two-factor model

Syntax

Price = swaptionbylg2f(ZeroCurve,a,b,sigma,eta,rho,Strike,ExerciseDate,Maturity)

Price = swaptionbylg2f(___,Name,Value)

Description

Price = swaptionbylg2f(ZeroCurve,a,b,sigma,eta,rho,Strike,ExerciseDate,Maturity) returns the European swaption price for a two-factor additive Gaussian interest-rate model.

Note

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

example

Price = swaptionbylg2f(___,Name,Value) adds optional name-value pair arguments.

example

Examples

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Price a European Swaption Using a Linear Gaussian Two-Factor Model

Open Live Script

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

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;
 
Reset = 1;
ExerciseDate = daysadd(Settle,360*5,1);
Maturity = daysadd(ExerciseDate,360*[3;4],1);
Strike = .05;
  
Price = swaptionbylg2f(irdc,a,b,sigma,eta,rho,Strike,ExerciseDate,Maturity,'Reset',Reset)

Price = 2×1

    1.1869
    1.5590

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

Data Types: single | double

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

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

Data Types: single | double

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

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

Data Types: single | double

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

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

Data Types: single | double

`rho` — Scalar correlation of the factors
scalar

Scalar correlation of the factors, specified as a scalar.

Data Types: single | double

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

Swaption strike price, specified as a nonnegative integer using a NumSwaptions-by-1 vector.

Data Types: single | double

`ExerciseDate` — Swaption exercise dates
datetime array | string array | date character vector

Swaption exercise dates, specified as a NumSwaptions-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, swaptionbylg2f also accepts serial date numbers as inputs, but they are not recommended.

`Maturity` — Underlying swap maturity date
datetime array | string array | date character vector

Underlying swap maturity date, specified using a NumSwaptions-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, swaptionbylg2f 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 = swaptionbylg2f(irdc,a,b,sigma,eta,rho,Strike,ExerciseDate,Maturity,'Reset',1,'Notional',100,'OptSpec','call')

`Reset` — Frequency of swaption 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 swaption 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 NumSwaptions-by-1 vector.

Data Types: single | double

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

Notional value of swaption, specified as the comma-separated pair consisting of 'Notional' and a nonnegative integer using a NumSwaptions-by-1 vector of notional amounts.

Data Types: single | double

`OptSpec` — Option specification for the swaption
`'call'` (default) | character vector with value of `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

Option specification for the swaption, specified as the comma-separated pair consisting of 'OptSpec' and a character vector or a NumSwaptions-by-1 cell array of character vectors with a value of 'call' or 'put'.

A 'call' swaption or Payer swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option pays the fixed rate and receives the floating rate.

A 'put' swaption or Receiver swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option receives the fixed rate and pays the floating rate.

Data Types: char | cell

Output Arguments

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`Price` — Swaption price
scalar | vector

Swaption price, returned as a scalar or an NumSwaptions-by-1 vector.

More About

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Call Swaption

A call swaption or payer swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option pays the fixed rate and receives the floating rate.

Put Swaption

A put swaption or receiver swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option receives the fixed rate and pays the floating rate.

Algorithms

The following defines the swaption price for a 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 swaptionbylg2f 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.

swaptionbylg2f

Syntax

Description

Examples

Price a European Swaption 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 the factors
scalar

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

`ExerciseDate` — Swaption exercise dates
datetime array | string array | date character vector

`Maturity` — Underlying swap maturity date
datetime array | string array | date character vector

Name-Value Arguments

`Reset` — Frequency of swaption 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 swaption
`100` (default) | nonnegative integer | vector of nonnegative integers

`OptSpec` — Option specification for the swaption
`'call'` (default) | character vector with value of `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

Output Arguments

`Price` — Swaption price
scalar | vector

More About

Call Swaption

Put Swaption

Algorithms

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

swaptionbylg2f

Syntax

Description

Examples

Price a European Swaption 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 the factors scalar

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

ExerciseDate — Swaption exercise dates datetime array | string array | date character vector

Maturity — Underlying swap maturity date datetime array | string array | date character vector

Name-Value Arguments

Reset — Frequency of swaption 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 swaption 100 (default) | nonnegative integer | vector of nonnegative integers

OptSpec — Option specification for the swaption 'call' (default) | character vector with value of 'call' or 'put' | cell array of character vectors with values of 'call' or 'put'

Output Arguments

Price — Swaption price scalar | vector

More About

Call Swaption

Put Swaption

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 the factors
scalar

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

`ExerciseDate` — Swaption exercise dates
datetime array | string array | date character vector

`Maturity` — Underlying swap maturity date
datetime array | string array | date character vector

`Reset` — Frequency of swaption 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 swaption
`100` (default) | nonnegative integer | vector of nonnegative integers

`OptSpec` — Option specification for the swaption
`'call'` (default) | character vector with value of `'call'` or `'put'` | cell array of character vectors with values of `'call'` or `'put'`

`Price` — Swaption price
scalar | vector