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Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is a statistical model used in analyzing time-series data where the variance error is believed to be serially autocorrelated. GARCH models assume that the variance of the error term follows an autoregressive moving average process.
Models used to price options account for variables such as current market price, strike price, volatility, interest rate, and time to expiration to theoretically value an option. Some commonly used models to value options are Black-Scholes, binomial option pricing, and Monte-Carlo simulation.
The Black-Scholes model, aka the Black-Scholes-Merton (BSM) model, is a differential equation widely used to price options contracts. The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.
GARCH option pricing model has three distinctive features. First, the GARCH option price is a function of the risk premium embedded in the underlying asset. This contrasts with the standard preference-free option pricing result. Second, the GARCH option pricing model is n~n-Markovian.
The Takeaway. The Heston model prices options using stochastic (random) volatility to more accurately model options pricing behavior. The more well-known Black-Scholes option pricing model assumes that implied volatility remains constant.
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The GARCH option-pricing model was first introduced by Duan (1995) with a locally risk-neutral valuation relationship (LRNVR), in which the conditional variances and model parameters remained the same under the physical measure and the risk-neutral measure.
Option pricing models are theories that can calculate the value of an options contract based on the number of variables within the actual contract. The key aim of a pricing model is to work out the probability of whether the option is in-the-money or out-of-the-money when it is exercised.
GARCH is a statistical model that can be used to analyze a number of different types of financial data, for instance, macroeconomic data. Financial institutions typically use this model to estimate the volatility of returns for stocks, bonds, and market indices.

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