Volatility modelling plays an important role in financial analysis, volatility is treated as a measurement to reflect the magnitude of risk in hedging, option pricing, and portfolio optimization. So it’s crucial to estimate and predict volatility correctly. During the last few decades, Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are quite popular, but due to the limitation of the models, they couldn’t describe the volatility properly, and the envelopes of them are changing irregularly. Many improved heteroscedasticity models were proposed. The Stochastic Volatility (SV) model shows a better performance, and also contributes to the generalization of the famous Black-Scholes (B-S) model.

In this thesis,...[ Read more ]

Volatility modelling plays an important role in financial analysis, volatility is treated as a measurement to reflect the magnitude of risk in hedging, option pricing, and portfolio optimization. So it’s crucial to estimate and predict volatility correctly. During the last few decades, Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are quite popular, but due to the limitation of the models, they couldn’t describe the volatility properly, and the envelopes of them are changing irregularly. Many improved heteroscedasticity models were proposed. The Stochastic Volatility (SV) model shows a better performance, and also contributes to the generalization of the famous Black-Scholes (B-S) model.

In this thesis, we compare the differences between some popular volatility models and try to model the volatility through the SV model, but from the state space perspective. With the help of the Kalman filter and Expectation-Maximization (EM) Algorithm, we regard the real volatility as a latent state of the model and model it with the observations. But sometimes there are convergence issues. Several approaches are proposed, aiming to solve the convergence issue and increase the accuracy, called Group SV and Scale SV. We also manipulate a component SV structure to capture more features in the model. Results on synthetic data and empirical data are provided to illustrate the performance evaluation.

Finally, our Kalman SV, Group SV, Scale SV, and Component SV model give smoother but more accurate envelope. The Group SV model is the most accurate; Scale SV model, considering both accuracy and time consuming, is much faster; finally, the Component SV model offers a framework to capture selected feature into the model, which is more flexible. All of our models have good performance in modelling and predicting the volatility, the results are also easier to be applied to option pricing.