volatilities

Compute implied volatilities when using SABR pricer

Syntax

outVolatilities = volatilities(inpPricer,ExerciseDate,ForwardValue,Strike)

Description

outVolatilities = volatilities(inpPricer,ExerciseDate,ForwardValue,Strike) computes implied volatilities for a Swaption instrument when you use a SABR pricer.

Examples

Compute Implied Volatilities for Swaption Instrument

This example shows the workflow to compute implied volatilities for a Swaption Instrument.

Create ratecurve Object

Create a ratecurve object using ratecurve.

ValuationDate = datetime(2016,3,5);
ZeroDates = datemnth(ValuationDate,[1 2 3 6 9 12*[1 2 3 4 5 6 7 8 9 10 12]])';
ZeroRates = [-0.33 -0.28 -0.24 -0.12 -0.08 -0.03 0.015 0.028 ...
            0.033 0.042 0.056 0.095 0.194 0.299 0.415 0.525]'/100;
Compounding = 1;
ZeroCurve = ratecurve("zero",ValuationDate,ZeroDates,ZeroRates,'Compounding',Compounding)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: 1
                Basis: 0
                Dates: [16×1 datetime]
                Rates: [16×1 double]
               Settle: 05-Mar-2016
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create SABR Model Object

Use finmodel to create a SABR model object.

Alpha = 0.0135;
Beta = 0.5;
Rho = 0.4654;
Nu = 0.4957;
Shift = 0.008;
 
SABRModel = finmodel("SABR",'Alpha',Alpha,'Beta',Beta,'Rho',Rho,'Nu',Nu,'Shift',Shift)

SABRModel = 
  SABR with properties:

             Alpha: 0.0135
              Beta: 0.5000
               Rho: 0.4654
                Nu: 0.4957
             Shift: 0.0080
    VolatilityType: "black"

Create SABR Pricer Object

Use finpricer to create a SABR pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

SABRPricer = finpricer("Analytic", 'Model', SABRModel,'DiscountCurve', ZeroCurve)

SABRPricer = 
  SABR with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.SABR]

Compute Implied Volatilities

Use volatilities to compute the implied volatilities for a Swaption instrument.

SwaptionExerciseDate = datetime(2017,3,5);
ForwardValue = 0.0007;
StrikeGrid = [-0.5; -0.25; -0.125; 0; 0.125; 0.25; 0.5; 1.0; 1.5]/100;
MarketStrikes = ForwardValue + StrikeGrid;

outVolatilities = volatilities(SABRPricer, SwaptionExerciseDate, ForwardValue, MarketStrikes)

outVolatilities = 9×1

    0.2132
    0.1500
    0.1409
    0.1474
    0.1609
    0.1752
    0.2004
    0.2372
    0.2627

Input Arguments

inpPricer — SABR pricer

SABR pricer object

SABR pricer, specified as a previously created SABR pricer object.

Data Types: object

ExerciseDate — Option exercise date

datetime scalar | string scalar | date character vector

Option exercise date, specified as a scalar datetime, string, or date character vector.

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

ForwardValue — Forward swap rate

decimal

Forward swap rate, specified as a scalar decimal.

Data Types: object

Strike — Strike rate

decimal

Strike rate, specified as a scalar decimal.

Data Types: double

Output Arguments

outVolatilities — Output volatilities

numeric

Output volatilities, returned as a numeric.

More About

Implied Volatility

Implied volatility is the market's expectations of the future volatility of the underlying asset's price over the life of an option.

Implied volatility is derived from the market price of an option using an options pricing model. Implied volatility is a key input for traders and investors as it helps gauge market sentiment and the potential for price fluctuations.

Version History

Introduced in R2020b

R2022b: Serial date numbers not recommended

Although volatilities 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.