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Some Aspects of Statistical Volatility Analysis

Some Aspects of Statistical Volatility Analysis

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Title: Some Aspects of Statistical Volatility Analysis
Author: Xu, Min
Abstract: Volatility is the key of the option price in the stock market. Changes in volatility will dramatically lead to changes of the option price.

One of the most important volatilities is historical volatility(HV). HV is essentially the annualized standard deviation of the first order difference of logarithm of the asset price. Therefore, changes in HV in finance may be detected by the variance change detection methods in statistics.

We propose a weighted sum of powers of variances method to detect single change in HV. It is noted that this method only examines if there is one single change-point in the data sequence. In the second part of the dissertation, we propose the empirical Bayesian information criterion (emBIC) method to detect multiple change-points simultaneously. The empirical BIC method can not only detect change-points in HV, but also in mean, and mean-and-variance. Simulation study shows that both of the above methods perform very well. We also apply these methods to detect changes in HV by using real stock data.

Another important volatility is the implied volatility (IV). IV is the volatility of asset implied by the market option price based on Black-Sholes model. The long term IV and HV have totally different behaviours. We find the optimal time range by using the emBIC method aforementioned above. We explain the long term IV behaviour by interest rate risk and capital charge in the last part of the dissertation.
Subject: Statistics
Applied mathematics
Keywords: implied volatility
historical volatility
interest rate risk
change-point
long term implied volatility behaviour
multiple change-points
Bayesian
MCMC
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/30740
Supervisor: Wu, Yuehua
Degree: PhD - Doctor of Philosophy
Program: Mathematics & Statistics
Exam date: 2015-08-28
Publish on: 2015-12-16

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