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price

Compute price for equity instrument with VannaVolga pricer

Since R2020b

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Syntax

[Price,PriceResult] = price(inpPricer,inpInstrument)
[Price,PriceResult] = price(___,inpSensitivity)

Description

[Price,PriceResult] = price(inpPricer,inpInstrument) computes the instrument price and related pricing information based on the pricing object inpPricer and the instrument object inpInstrument.

example

[Price,PriceResult] = price(___,inpSensitivity) adds an optional argument to specify sensitivities.

example

Examples

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Open Live Script

This example shows the workflow to price a DoubleBarrier instrument when you use a BlackScholes model and a VannaVolga pricing method.

Create DoubleBarrier Instrument Object

Use fininstrument to create a DoubleBarrier instrument object. 

DoubleBarrierOpt = fininstrument("DoubleBarrier",'Strike',100,'ExerciseDate',datetime(2020,8,15),'OptionType',"call",'ExerciseStyle',"European",'BarrierType',"DKO",'BarrierValue',[110 80],'Name',"doublebarrier_option")
DoubleBarrierOpt = 
  DoubleBarrier with properties:

       OptionType: "call"
           Strike: 100
     BarrierValue: [110 80]
    ExerciseStyle: "european"
     ExerciseDate: 15-Aug-2020
      BarrierType: "dko"
           Rebate: [0 0]
             Name: "doublebarrier_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object. 

BlackScholesModel = finmodel("BlackScholes","Volatility",0.02)
BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.0200
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve. 

Settle = datetime(2019,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create VannaVolga Pricer Object

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

VolRR = -0.0045;
VolBF = 0.0037;
RateF = 0.0210;
outPricer = finpricer("VannaVolga","DiscountCurve",myRC,"Model",BlackScholesModel,'SpotPrice',100,'DividendValue',RateF,'VolatilityRR',VolRR,'VolatilityBF',VolBF)
outPricer = 
  VannaVolga with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.BlackScholes]
        SpotPrice: 100
     DividendType: "continuous"
    DividendValue: 0.0210
     VolatilityRR: -0.0045
     VolatilityBF: 0.0037

Price DoubleBarrier Instrument

Use price to compute the price and sensitivities for the DoubleBarrier instrument.

[Price, outPR] = price(outPricer,DoubleBarrierOpt,["all"])
Price = 
1.6450

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]


outPR.Results 
ans=1×7 table
    Price     Delta     Gamma     Lambda     Vega      Theta      Rho  
    _____    _______    ______    ______    ______    _______    ______

    1.645    0.82818    75.662    50.346    14.697    -1.3145    74.666

Input Arguments

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Pricer object, specified as a scalar VannaVolga pricer object. Use finpricer to create the VannaVolga pricer object.

Data Types: object

Instrument object, specified as a scalar or vector of Vanilla, Barrier, DoubleBarrier, Touch, or DoubleTouch instrument objects. Use fininstrument to create the Vanilla, Barrier, DoubleBarrier, Touch, or DoubleTouch instrument objects.

Data Types: object

(Optional) List of sensitivities to compute, specified as a NOUT-by-1 or a 1-by-NOUT cell array of character vectors or string array with supported values.

inpSensitivity = {'All'} or inpSensitivity = ["All"] specifies that the output is 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'Price'. This is the same as specifying inpSensitivity to include each sensitivity.

Example: inpSensitivity = {'delta','gamma','vega','rho','lambda','theta','price'}

The sensitivities supported depend on the inpInstrument.

inpInstrumentSupported Sensitivities
Vanilla, 'delta','gamma','vega','rho','lambda','theta','price'
Barrier'delta','gamma','vega','rho','lambda','theta','price'
DoubleBarrier'delta','gamma','vega','rho','lambda','theta','price'
Touch'delta','gamma','vega','rho','lambda','theta','price'
DoubleTouch'delta','gamma','vega','rho','lambda','theta','price'

Data Types: string | cell

Output Arguments

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Instrument price, returned as a numeric.

Price result, returned as a PriceResult object. The object has the following fields:

  • PriceResult.Results — Table of results that includes sensitivities (if you specify inpSensitivity)

  • PriceResult.PricerData — Structure for pricer data

  • PriceResult.PricerData.Overhedge — TBD

More About

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Delta

A delta sensitivity measures the rate at which the price of an option is expected to change relative to a $1 change in the price of the underlying asset.

Delta is not a static measure; it changes as the price of the underlying asset changes (a concept known as gamma sensitivity), and as time passes. Options that are near the money or have longer until expiration are more sensitive to changes in delta.

Gamma

A gamma sensitivity measures the rate of change of an option's delta in response to a change in the price of the underlying asset.

In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. This is important because this helps you understand the convexity of an option's value in relation to the underlying asset's price.

Vega

A vega sensitivity measures the sensitivity of an option's price to changes in the volatility of the underlying asset.

Vega represents the amount by which the price of an option would be expected to change for a 1% change in the implied volatility of the underlying asset. Vega is expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls.

Theta

A theta sensitivity measures the rate at which the price of an option decreases as time passes, all else being equal.

Theta is essentially a quantification of time decay, which is a key concept in options pricing. Theta provides an estimate of the dollar amount that an option's price would decrease each day, assuming no movement in the price of the underlying asset and no change in volatility.

Rho

A rho sensitivity measures the rate at which the price of an option is expected to change in response to a change in the risk-free interest rate.

Rho is expressed as the amount of money an option's price would gain or lose for a one percentage point (1%) change in the risk-free interest rate.

Lambda

A lambda sensitivity measures the percentage change in an option's price for a 1% change in the price of the underlying asset.

Lambda is a measure of leverage, indicating how much more sensitive an option is to price movements in the underlying asset compared to owning the asset outright.

Version History

Introduced in R2020b

See Also

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