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The challenging process in modelling asset prices is dealing with the characteristic data that are dynamics and non-Gaussian. Especially, some data on certain stocks that have jumped. Therefore, a model that can handle such fluctuating data is needed. The jump Diffusion Model can be used because it is suitable for the characteristic of the stock price that is not normally distributed and volatile. Therefore, this study aims to predict and forecast the market's prices accurately using Jump-Diffusion Model. This research can conclude that the model performs well in modelling the data. [ABSTRACT FROM AUTHOR]

This study aims to predict the price of stock options in the future period when the underlying asset follows a Garch process and as a consideration for stock traders to make decisions to sell or buy options for a stock. GARCH Model can forecast volatility which is needed in financial applications. We select the best GARCH Model based on AIC and BIC value for the underlying stock and embedding it into the Monte Carlo scheme to derive price Asian option. We use data on ISSP to illustrate fat tail and volatility data. The result shows that the best GARCH Model for the historical data ISSP stock is ARMA-GARCH. [ABSTRACT FROM AUTHOR]