price
Compute price for equity instrument with NumericalIntegration
pricer
Since R2020a
Syntax
Description
[
computes the instrument price and related pricing information based on the pricing object
Price
,PriceResult
] = price(inpPricer
,inpInstrument
)inpPricer
and the instrument object
inpInstrument
.
[
adds an optional argument to specify sensitivities.Price
,PriceResult
] = price(___,inpSensitivity
)
Examples
Use NumericalIntegration
Pricer and Merton
Model to Price Vanilla
Instrument
This example shows the workflow to price a Vanilla
instrument when you use a Merton
model and a NumericalIntegration
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2020,3,15),'ExerciseStyle',"european",'Strike',105,'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Mar-2020 Strike: 105 Name: "vanilla_option"
Create Merton
Model Object
Use finmodel
to create a Merton
model object.
MertonModel = finmodel("Merton",'Volatility',0.45,'MeanJ',0.02,'JumpVol',0.07,'JumpFreq',0.09)
MertonModel = Merton with properties: Volatility: 0.4500 MeanJ: 0.0200 JumpVol: 0.0700 JumpFreq: 0.0900
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
myRC = ratecurve('zero',datetime(2019,9,15),datetime(2020,3,15),0.02)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: 15-Mar-2020 Rates: 0.0200 Settle: 15-Sep-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create NumericalIntegration
Pricer Object
Use finpricer
to create a NumericalIntegration
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("numericalintegration",'Model',MertonModel,'DiscountCurve',myRC,'SpotPrice',100,'DividendValue',.01,'VolRiskPremium',0.9,'LittleTrap',false,'AbsTol',0.5,'RelTol',0.4,'Framework',"lewis2001")
outPricer = NumericalIntegration with properties: Model: [1x1 finmodel.Merton] DiscountCurve: [1x1 ratecurve] SpotPrice: 100 DividendType: "continuous" DividendValue: 0.0100 AbsTol: 0.5000 RelTol: 0.4000 IntegrationRange: [1.0000e-09 Inf] CharacteristicFcn: @characteristicFcnMerton76 Framework: "lewis2001" VolRiskPremium: 0.9000 LittleTrap: 0
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 10.7325
outPR = priceresult with properties: Results: [1x6 table] PricerData: []
outPR.Results
ans=1×6 table
Price Delta Gamma Theta Rho Vega
______ ______ ________ _______ ______ ______
10.732 0.5058 0.012492 -12.969 19.815 27.954
Input Arguments
inpPricer
— Pricer object
NumericalIntegration
object
Pricer object, specified as a scalar NumericalIntegration
pricer object. Use finpricer
to create the NumericalIntegration
pricer object.
Data Types: object
inpInstrument
— Instrument object
Vanilla
object
Instrument object, specified as a scalar or vector of Vanilla
instrument objects.
Use fininstrument
to create
Vanilla
instrument
objects.
Data Types: object
inpSensitivity
— List of sensitivities to compute
[ ]
(default) | string array with values "Price"
, "Delta"
,
"Gamma"
, "Vega"
, "Rho"
,
"Theta"
, "Vegalt"
, and
"All"
| cell array of character vectors with values 'Price'
,
'Delta'
, 'Gamma'
, 'Vega'
,
'Rho'
, 'Theta'
, 'Vegalt'
, and
'All'
(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 possible values of 'Price'
,
'Delta'
, 'Gamma'
, 'Vega'
,
'Rho'
, 'Theta'
, 'Vegalt'
, and
'All'
.
inpSensitivity = {'All'}
or inpSensitivity =
["All"]
specifies that the output is 'Delta'
,
'Gamma'
, 'Vega'
, 'Rho'
,
'Theta'
, 'Vegalt'
, and
'Price'
. This is the same as specifying
inpSensitivity
to include each sensitivity.
Example: inpSensitivity =
{'delta','gamma','vega','rho','theta','vegalt','price'}
Data Types: string
| cell
Output Arguments
Price
— Instrument price
numeric
Instrument price, returned as a numeric.
PriceResult
— Price result
PriceResult
object
Price result, returned as an object. The PriceResult
object. The
object has the following fields:
PriceResult.Results
— Table of results that includes sensitivities (if you specifyinpSensitivity
)PriceResult.PricerData
— Structure for pricer data
More About
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.
Vegalt
A vegalt sensitivity measures the sensitivity of an option's price to changes in the long-term volatility of the underlying asset.
Version History
Introduced in R2020a
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