Realized GARCH Model in Volatility Forecasting and Option Pricing

We have developed a novel option pricing model that relies on forecasting realized volatility. By incorporating past conditional volatility from the underlying asset based on the GARCH model, we address heteroscedasticity in time-varying realized volatility. To overcome the GARCH model's inability to capture the long-range persistence of volatility in financial time series, our model leverages the additive cascade model for estimating realized volatility components across various frequencies. Easily estimated from historical data, our model's parameters yield forecasts with reduced measurement error and accurately capture the time series pattern of volatility in financial data. Additionally, our model can be adapted as a new option pricing method based on discrete-time stochastic volatility. We obtain martingale measures and option prices through Monte Carlo simulations. In our empirical analysis, we applied this model to the S & P 500 equity index, Nasdaq, and Dow Jones Industrial Average market indices. We also explored the model's application in pricing European options for the S & P 500 market index.