# Heston

Create `Heston`

pricer object for
`VarianceSwap`

instrument using `Heston`

model

*Since R2020b*

## Description

Create and price a `VarianceSwap`

instrument object with a
`Heston`

model and a `Heston`

pricing method using
this workflow:

Use

`fininstrument`

to create a`VarianceSwap`

instrument object.Use

`finmodel`

to specify the`Heston`

model for the`VarianceSwap`

instrument object.Use

`finpricer`

to specify the`Heston`

pricer object for the`VarianceSwap`

instrument object.

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 instruments, models, and pricing methods for a
`VarianceSwap`

instrument, see Choose Instruments, Models, and Pricers.

## Creation

### Description

creates a `HestonPricerObj`

= finpricer(`PricerType`

,'`DiscountCurve`

',ratecurve_obj,'`Model`

',model)`Heston`

pricer object by specifying
`PricerType`

and sets properties using the
required name-value pair arguments `DiscountCurve`

and
`Model`

. For example, ```
HestonPricerObj =
finpricer("Analytic",'DiscountCurve',ratecurve_obj,'Model',HWModel)
```

creates a `Heston`

pricer object.

### Input Arguments

## Properties

## Object Functions

`price` | Compute price for interest-rate, equity, or credit derivative instrument with
`Analytic` pricer |

## Examples

## Algorithms

Variance swaps can be priced with the calibrated Heston model by using the following closed-form expression for the fair variance:

$${K}_{\mathrm{var}}=\frac{1-{e}^{-kT}}{kT}({n}_{0}-\theta )+\theta $$

Here:

*ν*_{0}is the initial variance of the underlying asset at*𝑡*= 0*ν*_{0}> 0.θ is the long-term variance level θ > 0.

*k*is the mean reversion speed for the variance (*k*> 0).

Once the fair variance is computed, the actual price paid in the market at time
*t* for the variance swap with a start date at time 0 is computed
as follows:

$$VarianceSwap(t)=Notional\times Disc(t,T)\times \left[\frac{t}{T}RealizedVariance(0,t)+\frac{T-t}{T}FairVariance(t,T)-StrikeVariance\right]$$

Here:

*t*is the time from the start date of the variance swap to the settle date.*T*is the time from the start date to the maturity date of the variance swap.*Disc*(*t*,*T*) is the discount factor from settle to the maturity date.*RealizedVariance*(0,*t*) is the realized variance from start date to the settle date, in basis points.*FairVariance*(*t*,*T*) is the fair variance for the remaining life of the contract as of the settle date, in basis points.*StrikeVariance*is the strike variance predetermined at inception (start date), in basis points.

## Version History

**Introduced in R2020b**