VarianceSwap

VarianceSwap instrument object

Description

Create and price a VarianceSwap instrument object using this workflow:

1. Use fininstrument to create a VarianceSwap instrument object.

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

3. When using a curve model, use finpricer to specify a ReplicatingVarianceSwap pricing method for the VarianceSwap instrument.

   When using a Heston model, use finpricer to specify a Heston pricing method for the VarianceSwap instrument.

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 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" | character vector with value 'VarianceSwap'

Instrument type, specified as a string with the value of "VarianceSwap" or a character vector with the value of 'VarianceSwap'.

Data Types: char | string

VarianceSwap Name-Value Pair Arguments

Specify required and optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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 | serial date number | date character vector | date string

Variance swap maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, serial date number, date character vector, or date string.

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

Data Types: char | double | string | datetime

'Notional' — Notional amount

numeric

Notional amount, specified as the comma-separated pair consisting of 'Notional' and a scalar numeric.

Data Types: double

Optional VarianceSwap Name-Value Pair Arguments

'StartDate' — Start date

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

Start date, specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, serial date number, date character vector, or date string.

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

Data Types: double | char | string | datetime

'RealizedVariance' — Realized variance

0 (default) | decimal

Realized variance, specified as the comma-separated pair consisting of 'RealizedVariance' and a scalar decimal.

Data Types: double

'Strike' — Strike variance

fair variance computed by pricer (default) | decimal

Strike variance, specified as the comma-separated pair consisting of 'Strike' and a scalar decimal.

Data Types: double

'Name' — User-defined name for instrument

" " (default) | string | character vector

User-defined name for the instrument, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector.

Data Types: char | string

Properties

Maturity — Maturity date

datetime

Maturity date, returned as a datetime.

Data Types: datetime

Notional — Notional amount

numeric

Notional amount, returned as a scalar numeric.

Data Types: double

StartDate — Start date

Settle date of the ratecurve (default) | datetime

Start date, returned as a datetime.

Data Types: double | char | string | datetime

RealizedVariance — Realized variance

0 (default) | decimal

Realized variance, returned as a scalar decimal.

Data Types: double

Strike — Strike variance

fair variance computed by pricer (default) | decimal

Strike variance, returned as a scalar decimal.

Data Types: double

Name — User-defined name for instrument

" " (default) | string

User-defined name for the instrument, returned as a string.

Data Types: string

Object Functions

Examples

Price Variance Swap 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 Variance Swap Instrument Using ratecurve and Replicating Variance Swap 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

VarianceSwap

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

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.