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.

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

Examples

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

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

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

Price — Swaption price

scalar | vector

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

More About

Swaption

A swaption (swap option) is a financial derivative that gives the holder the right, but not the obligation, to enter into an interest-rate swap agreement at a specified future date and under predetermined terms.

Swaptions are used by investors and institutions to hedge against interest rate fluctuations or to speculate on future changes in interest rates.

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:

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

$$dx(t)=-ax(t)dt+\sigma d{W}_1(t),x(0)=0$$

$$dy(t)=-by(t)dt+\eta d{W}_2(t),y(0)=0$$

where $$d{W}_1(t)d{W}_2(t)=\rho dt$$ 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

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.