VarianceSwap

VarianceSwap instrument object

Since R2020b

Description

Create and price a VarianceSwap instrument object for one or more Variance Swap instruments using this workflow:

1. Use fininstrument to create a VarianceSwap instrument object for one or more Variance Swap instruments.

2. Use ratecurve to specify a curve model or use finmodel to specify a Heston model.

3. Choose a pricing method.

   • When using a curve model, use finpricer to specify a ReplicatingVarianceSwap pricing method for one or more VarianceSwap instruments.

   • When using a Heston model, use finpricer to specify a Heston pricing method for one or more VarianceSwap instruments.

For more information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

For more information on the available models and pricing methods for a VarianceSwap instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

VarianceSwapInstrument = fininstrument(InstrumentType,'Maturity',maturity_date,'Notional',notional_value)

VarianceSwapInstrument = fininstrument(___,Name,Value)

Description

VarianceSwapInstrument = fininstrument(InstrumentType,'Maturity',maturity_date,'Notional',notional_value) creates a VarianceSwap object for one or more Variance Swap instruments by specifying InstrumentType and sets properties using the required name-value pair arguments Maturity and Notional.

The VarianceSwap instrument supports the ReplicatingVarianceSwap and Heston pricing methods. For more information on the VarianceSwap instrument, see More About.

VarianceSwapInstrument = fininstrument(___,Name,Value) sets optional properties using additional name-value pair arguments in addition to the required arguments in the previous syntax. For example, VarianceSwapInstrument = fininstrument("VarianceSwap",'Maturity',datetime(2019,1,30),'Notional',100,'StartDate',datetime(2016,1,30),'RealizedVariance',0.02,'Strike',110,'Name',"varianceswap_instrument") creates a VarianceSwap option with a maturity date of January 30, 2019. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

string with value "VarianceSwap" | string array with values of "VarianceSwap" | character vector with value 'VarianceSwap' | cell array of character vectors with values of 'VarianceSwap'

Instrument type, specified as a string with the value of "VarianceSwap", a character vector with the value of 'VarianceSwap', an NINST-by-1 string array with values of "VarianceSwap", or an NINST-by-1 cell array of character vectors with values of 'VarianceSwap'.

Data Types: char | cell | string

Name-Value Arguments

Specify required and 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: VarianceSwapInstrument = fininstrument("VarianceSwap",'Maturity',datetime(2019,1,30),'Notional',100,'StartDate',datetime(2016,1,30),'RealizedVariance',0.02,'Strike',110,'Name',"varianceswap_instrument")

Required VarianceSwap Name-Value Pair Arguments

Maturity — Variance swap maturity date

datetime array | string array | date character vector

Variance swap maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar or an NINST-by-1 vector.

If you use date character vectors or strings, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

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

Notional — Notional amount

scalar numeric | numeric vector

Notional amount, specified as the comma-separated pair consisting of 'Notional' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Optional VarianceSwap Name-Value Pair Arguments

StartDate — Start date

Settle date of the ratecurve (default) | datetime array | string array | date character vector

Start date, specified as the comma-separated pair consisting of 'StartDate' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

If you use date character vectors or strings, the format must be recognizable by datetime because the ExerciseDate property is stored as a datetime.

RealizedVariance — Realized variance

0 (default) | scalar decimal | decimal vector

Realized variance, specified as the comma-separated pair consisting of 'RealizedVariance' and a scalar decimal or an NINST-by-1 vector of decimals.

Data Types: double

Strike — Strike variance

fair variance computed by pricer (default) | scalar decimal | decimal vector

Strike variance, specified as the comma-separated pair consisting of 'Strike' and a scalar decimal or an NINST-by-1 vector of decimals.

Data Types: double

Name — User-defined name for instrument

" " (default) | string | string array | character vector | cell array of character vectors

User-defined name for one of more instruments, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: char | cell | string

Properties

Maturity — Maturity date

datetime | vector of datetimes

Maturity date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Notional — Notional amount

scalar numeric | numeric vector

Notional amount, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

StartDate — Start date

Settle date of the ratecurve (default) | datetime | vector of datetimes

Start date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

RealizedVariance — Realized variance

0 (default) | scalar decimal | decimal vector

Realized variance, returned as a scalar decimal or an NINST-by-1 decimal vector.

Data Types: double

Strike — Strike variance

fair variance computed by pricer (default) | scalar decimal | decimal vector

Strike variance, returned as a scalar decimal or an NINST-by-1 decimal vector.

Data Types: double

Name — User-defined name for instrument

" " (default) | string | string array

User-defined name for the instrument, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Object Functions

Examples

Price VarianceSwap Instrument Using Heston Model and Heston Pricer

This example shows the workflow to price a VarianceSwap instrument when you use a Heston model and a Heston pricing method.

Create VarianceSwap Instrument Object

Use fininstrument to create a VarianceSwap instrument object.

VarianceSwapInst = fininstrument("VarianceSwap",'Maturity',datetime(2020,9,15),'Notional',100,'StartDate',datetime(2020,6,15),'RealizedVariance',0.02,'Strike',0.05,'Name',"variance_swap_instrument")

VarianceSwapInst = 
  VarianceSwap with properties:

            Notional: 100
    RealizedVariance: 0.0200
              Strike: 0.0500
           StartDate: 15-Jun-2020
            Maturity: 15-Sep-2020
                Name: "variance_swap_instrument"

Create Heston Model Object

Use finmodel to create a Heston model object.

HestonModel = finmodel("Heston",'V0',0.06,'ThetaV',0.1,'Kappa',0.9,'SigmaV',0.7,'RhoSV',-.3)

HestonModel = 
  Heston with properties:

        V0: 0.0600
    ThetaV: 0.1000
     Kappa: 0.9000
    SigmaV: 0.7000
     RhoSV: -0.3000

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2020, 1, 1);
ZeroTimes = calmonths(3);
ZeroRates = 0.05;
ZeroDates = Settle + ZeroTimes;
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,'Basis',Basis)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Apr-2020
                Rates: 0.0500
               Settle: 01-Jan-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Heston Pricer Object

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

outPricer = finpricer("Analytic",'DiscountCurve',ZeroCurve,'Model',HestonModel)

outPricer = 
  Heston with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.Heston]

Price VarianceSwap Instrument

Use price to compute the price and fair variance for the VarianceSwap instrument.

[Price, outPR] = price(outPricer,VarianceSwapInst,["all"])

Price = 
10.8321

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

outPR.Results

ans=1×2 table
    Price     FairVariance
    ______    ____________

    10.832      0.07039   

Price Multiple VarianceSwap Instruments Using Heston Model and Heston Pricer

This example shows the workflow to price multiple VarianceSwap instrument when you use a Heston model and a Heston pricing method.

Create VarianceSwap Instrument Object

Use fininstrument to create a VarianceSwap instrument object for three Variance Swap instruments.

VarianceSwapInst = fininstrument("VarianceSwap",'Maturity',datetime([2020,9,15 ; 2020,9,15 ; 2020,9,15]),'Notional',100,'StartDate',datetime(2020,6,15),'RealizedVariance',0.02,'Strike',0.05,'Name',"variance_swap_instrument")

VarianceSwapInst=3×1 VarianceSwap array with properties:
    Notional
    RealizedVariance
    Strike
    StartDate
    Maturity
    Name

Create Heston Model Object

Use finmodel to create a Heston model object.

HestonModel = finmodel("Heston",'V0',0.06,'ThetaV',0.1,'Kappa',0.9,'SigmaV',0.7,'RhoSV',-.3)

HestonModel = 
  Heston with properties:

        V0: 0.0600
    ThetaV: 0.1000
     Kappa: 0.9000
    SigmaV: 0.7000
     RhoSV: -0.3000

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2020, 1, 1);
ZeroTimes = calmonths(3);
ZeroRates = 0.05;
ZeroDates = Settle + ZeroTimes;
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,'Basis',Basis)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Apr-2020
                Rates: 0.0500
               Settle: 01-Jan-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Heston Pricer Object

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

outPricer = finpricer("Analytic",'DiscountCurve',ZeroCurve,'Model',HestonModel)

outPricer = 
  Heston with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.Heston]

Price VarianceSwap Instruments

Use price to compute the prices and fair variance for the three VarianceSwap instruments.

% [Price, outPR] = price(outPricer,VarianceSwapInst,["all"])
% outPR.Results

Price VarianceSwap Instrument Using ratecurve and ReplicatingVarianceSwap Pricer

This example shows the workflow to price a VarianceSwap instrument when you use a ratecurve object and a ReplicatingVarianceSwap pricing method.

Create VarianceSwap Instrument Object

Use fininstrument to create a VarianceSwap instrument object.

VarianceSwapInst = fininstrument("VarianceSwap",'Maturity',datetime(2021,5,1),'Notional',150,'StartDate',datetime(2020,5,1),'RealizedVariance',0.05,'Strike',0.1,'Name',"variance_swap_instrument")

VarianceSwapInst = 
  VarianceSwap with properties:

            Notional: 150
    RealizedVariance: 0.0500
              Strike: 0.1000
           StartDate: 01-May-2020
            Maturity: 01-May-2021
                Name: "variance_swap_instrument"

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2020, 9, 15);
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])];
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,'Basis',Basis)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create ReplicatingVarianceSwap Pricer Object

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

Strike = (50:5:135)';
Volatility = [.49;.45;.42;.38;.34;.31;.28;.25;.23;.21;.2;.21;.21;.22;.23;.24;.25;.26];
VolatilitySmile = table(Strike, Volatility);
SpotPrice = 100;
CallPutBoundary = 100;

outPricer =  finpricer("ReplicatingVarianceSwap",'DiscountCurve', ZeroCurve, 'VolatilitySmile', VolatilitySmile, ...
'SpotPrice', SpotPrice, 'CallPutBoundary', CallPutBoundary)

outPricer = 
  ReplicatingVarianceSwap with properties:

      DiscountCurve: [1x1 ratecurve]
       InterpMethod: "linear"
    VolatilitySmile: [18x2 table]
          SpotPrice: 100
    CallPutBoundary: 100

Price VarianceSwap Instrument

Use price to compute the price and fair variance for the VarianceSwap instrument.

[Price, outPR] = price(outPricer,VarianceSwapInst,["all"])

Price = 
8.1997

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: [1x1 struct]

outPR.Results

ans=1×2 table
    Price     FairVariance
    ______    ____________

    8.1997      0.21701   

More About

Variance Swap

A variance swap is a forward contract on the realized variance over time.

A variance swap is based on the volatility or variance of an underlying asset, which is typically a stock index, equity, or other financial instrument. Volatility represents the magnitude of price fluctuations of the underlying asset.

The variance swap's value is determined by the difference between the realized or expected variance of the underlying asset's price and a pre-defined strike variance level. The variance is calculated based on the square of the asset's returns over a specific period.

The payoff of a variance swap is based on the difference between the actual or expected variance and the strike variance. If the realized or expected variance is higher than the strike variance, the holder of the variance swap receives a positive payoff. Conversely, if the variance is lower than the strike, the holder pays the counterparty.

At expiration, the payoff of a variance swap is $$({\sigma }_R^2-K_{\mathrm{var}})\times \text{N}$$

Here:

σ²_R is the realized variance of the underlying asset (for example a stock or equity index) over the life of the contract.

K_var is the strike (contractual) variance that is set at the beginning of the contract to make the starting value equal to zero.

N is the notional amount.

Version History

Introduced in R2020b

R2022b: Serial date numbers not recommended

Although VarianceSwap 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.