THESIS
2022
1 online resource (xi, 49 pages) : illustrations (some color)
Abstract
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,...[
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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.
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