Get Heston Nandi 1997 - A Closed-form Garch Option Pricing Model - Bficl

The main advantage of the GARCH model is that it has much less parameters and performs better than the ARCH model. The generalized autoregressive conditional heteroskedasticity (GARCH) model has only three parameters that allow for an infinite number of squared roots to influence the conditional variance.

GARCH is a statistical modeling technique used to help predict the volatility of returns on financial assets. GARCH is appropriate for time series data where the variance of the error term is serially autocorrelated following an autoregressive moving average process.

Under ASC 718, stock price volatility is considered when calculating an option's fair value. In the Black-Scholes model, an option's fair value will equal its minimum value when volatility is assumed to be zero, or a number very close to zero.

GARCH is the most popular method to find volatility in stock prices. In the extensive literature, financial modeled considered as an autoregressive approach with conditional heteroskedasticity variation in the GARCH process.

The GARCH model is used to predict a level of volatility at a given time, and the proportion of risky vs risk-free assets is adjusted based on whether the predicted volatility value is higher or lower than the target value.

In the ARCH(q) process the conditional variance is specified as a linear function of past sample variances only, whereas the GARCH(p, q) process allows lagged conditional variances to enter as well. This corresponds to some sort of adaptive learning mechanism.

the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well-documented systematic biases associated with the Black-Scholes model.