Heston option pricing model matlab

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MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. This constructor creates and displays heston objects, which derive from the sdeddo SDE from drift and diffusion objects class. Use heston objects to simulate sample paths of two state variables. Each state variable is driven by a single Brownian motion source of risk over NPERIODS consecutive observation periods, approximating continuous-time stochastic volatility processes.

Heston models are bivariate composite models. Each Heston model consists of two coupled univariate models:. A geometric Brownian motion gbm model with a stochastic volatility function. This model usually corresponds to a price process whose volatility variance rate is governed by the second univariate model. A Cox-Ingersoll-Ross cir square root diffusion model. Specifying an array indicates a static non-time-varying parametric specification. This array fully captures all implementation details, which are clearly associated with a parametric form.

Specifying a function provides indirect support for virtually any static, dynamic, linear, or nonlinear model. This parameter is supported via an interface, because all implementation details are hidden and fully encapsulated by the function. You can specify combinations of array and function input parameters as needed. Moreover, a parameter is identified as a deterministic function of time if the function accepts a scalar time t as its only input argument.

Otherwise, a parameter is assumed to be a function of time t and state X t and is invoked with both input arguments.

If you specify Return as a scalar, it represents the expected mean instantaneous rate of return of the univariate GBM price model. As a deterministic function of time, when Return is called with a real-valued scalar time t as its only input, Return must produce a scalar. If you specify it as a function of time and state, Return calculates the instantaneous rate of return of the GBM price model. This function generates a scalar when invoked with two inputs:.

A 2 -by- 1 bivariate state vector X t.

heston option pricing model matlab

If you specify Speed as a scalar, it represents the mean-reversion speed of the univariate CIR stochastic variance model the speed at which the CIR variance reverts to its long-run average level. As a deterministic function of time, when Speed is called with a real-valued scalar time t as its only input, Speed must produce a scalar.

If you specify it as a function time and state, Speed calculates the speed of mean reversion of the CIR variance model. A 2 -by- 1 state vector X t. If you specify Level as a scalar, it represents the reversion level of the univariate CIR stochastic variance model.

As a deterministic function of time, when Level is called with a real-valued scalar time t as its only input, Level must produce a scalar. If you specify it as a function time and state, Level calculates the reversion level of the CIR variance model. If you specify Volatility as a scalar, it represents the instantaneous volatility of the CIR stochastic variance model, often called the volatility of volatility or volatility of variance.

Stochastic Volatility (SV)

As a deterministic function of time, when Volatility is called with a real-valued scalar time t as its only input, Volatility must produce a scalar. If you specify it as a function time and state, Volatility generates a scalar when invoked with two inputs:. Although the constructor does not enforce restrictions on the signs of any of these input arguments, each argument is specified as a positive value. The following rules apply when specifying parameter-name pairs:.

Option Price Calculator

Scalar, 2 -by- 1 column vector, or 2 -by- NTRIALS matrix of initial values of the state variables. If StartState is a scalar, heston applies the same initial value to both state variables on all trials.

If StartState is a bivariate column vector, heston applies a unique initial value to each state variable on all trials.

If StartState is a matrix, heston applies a unique initial value to each state variable on each trial. If you do not specify a value for StartState , all variables start at 1. Correlation between Gaussian random variates drawn to generate the Brownian motion vector Wiener processes.

Specify Correlation as a scalar, a 2 -by- 2 positive semidefinite matrix, or as a deterministic function C t that accepts the current time t and returns a 2 -by- 2 positive semidefinite correlation matrix.

Heston Option Pricer - File Exchange - MATLAB Central

As a deterministic function of time, Correlation allows you to specify a dynamic correlation structure. If you do not specify a value for Correlation , the default is a 2 -by- 2 identity matrix representing independent Gaussian processes. Access function for the Correlation input, callable as a function of time. Composite diffusion-rate function, callable as a function of time and state.

heston option pricing model matlab

Access function for the input argument Return , callable as a function of time and state. Access function for the input argument Speed , callable as a function of time and state. Access function for the input argument Level , callable as a function of time and state. Access function for the input argument Volatility , callable as a function of time and state.

ADI Schemes for Pricing Options under the Heston model - Karel in't Hout

Monte Carlo Methods in Financial Engineering. New York, Springer-Verlag, Options, Futures, and Other Derivatives , 5th ed. Stochastic Calculus for Finance II: Run the command by entering it in the MATLAB Command Window.

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Description This constructor creates and displays heston objects, which derive from the sdeddo SDE from drift and diffusion objects class. Each Heston model consists of two coupled univariate models: Input Arguments Specify required input parameters as one of the following types: The required input parameters are: Return If you specify Return as a scalar, it represents the expected mean instantaneous rate of return of the univariate GBM price model.

This function generates a scalar when invoked with two inputs: A real-valued scalar observation time t. Speed If you specify Speed as a scalar, it represents the mean-reversion speed of the univariate CIR stochastic variance model the speed at which the CIR variance reverts to its long-run average level.

Level If you specify Level as a scalar, it represents the reversion level of the univariate CIR stochastic variance model. Volatility If you specify Volatility as a scalar, it represents the instantaneous volatility of the CIR stochastic variance model, often called the volatility of volatility or volatility of variance. If you specify it as a function time and state, Volatility generates a scalar when invoked with two inputs: The following rules apply when specifying parameter-name pairs: Specify the parameter name as a character vector, followed by its corresponding parameter value.

Parameter names are case insensitive. You can specify unambiguous partial character vector matches. The following table lists valid parameter names.

StartTime Scalar starting time of the first observation, applied to all state variables. If you do not specify a value for StartTime , the default is 0. StartState Scalar, 2 -by- 1 column vector, or 2 -by- NTRIALS matrix of initial values of the state variables. Correlation Correlation between Gaussian random variates drawn to generate the Brownian motion vector Wiener processes.

A Correlation matrix represents a static condition. Simulation A user-defined simulation function or SDE simulation method. If you do not specify a value for Simulation , the default method is simulation by Euler approximation simByEuler.

Output Arguments heston Object of class heston with the following displayed parameters: Initial observation time StartState: Initial state at StartTime Correlation: Access function for the Correlation input, callable as a function of time Drift: Composite drift-rate function, callable as a function of time and state Diffusion: Composite diffusion-rate function, callable as a function of time and state Simulation: A simulation function or method Return: Access function for the input argument Return , callable as a function of time and state Speed: Access function for the input argument Speed , callable as a function of time and state Level: Access function for the input argument Level , callable as a function of time and state Volatility: Examples See Creating Heston Stochastic Volatility Models.

See Also cir gbm sdeddo Topics Simulating Equity Prices Simulating Interest Rates Stratified Sampling Pricing American Basket Options by Monte Carlo Simulation Base SDE Models Drift and Diffusion Models Linear Drift Models Parametric Models SDEs SDE Models SDE Class Hierarchy Performance Considerations. You clicked a link that corresponds to this MATLAB command: Was this topic helpful?

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Support MATLAB Answers Installation Help Bug Reports Product Requirements Software Downloads. Scalar starting time of the first observation, applied to all state variables. A user-defined simulation function or SDE simulation method. Object of class heston with the following displayed parameters:

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