Article by: Jim Gatheral, Merrill Lynch
Published by: Courant Institute of Mathematical Sciences
Date: 2001
“Although variance and volatility swaps are relatively recent innovations, there is already significant literature describing these contracts and the practicalities of hedging them.
“In fact, a variance swap is not really a swap at all but a forward contract on the realized annualized variance.”
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Article by: Tim Edwards PhD, Craig J. Lazzara CFA
Published by: McGraw Hill Financial
Date: Dec 2013
“With apologies to Jane Austen, it is a truth universally acknowledged that a portfolio manager in control of a fortune must be in want of diversification. But what does it mean to say that a particular index (or portfolio) is diversified? Or more diversified than another, or more now than it was before? In order to speak meaningfully about the internal diversity of an index and its variation over time, quantitative metrics are required. The most commonly encountered is the correlation statistic, but correlations contain critical and unavoidable flaws. It turns out that another measure—asset dispersion—has strong qualifications as a complementary tool.
“In what follows, we’ll show how dispersion can be used to examine the connection between active management performance and the idiosyncrasies present within underlying markets. We’ll also demonstrate other interesting uses of dispersion, which is well-suited to address questions regarding the importance of various risk factors and exposures.”
Full article (PDF): Link
Article by: Hong Xie, Jian Li
From: Brunel University
Published by: International Journal of Economics and Finance
Date: 2010
“This paper analysed intraday volatility by S&P 500 stock index future product and basic on the high frequency
trading strategy. The processes of the model are the GARCH series which including GARCH (1, 1), EGARCH
and IGARCH, moreover run such models again by GARCH-In-Mean process. The result presented that
EGARCH model is the preferred one of intraday volatility estimation in S&P500 stock index future product.
And IGARCH Model is the better one in in-the-sample estimation. Otherwise the IGARCH model is the
preferred for estimation in out-of sample and EGARCH model is the better one. GARCH (1, 1) model haven’t
good performance in the testing. Overall the result will engaged in microstructure market analysis and volatility
arbitrage in high frequency trading strategy. ”
Full article: Link
Article by: David Ruppert
From: Statistics and Data Analysis for Financial Engineering
Published by: Springer New York
Date: 2010
“…financial markets data often exhibit volatility clustering, where time series show periods of high volatility and periods of low volatility;…. In fact, with economic and financial data, time-varying volatility is more common than constant volatility, and accurate modeling of time-varying volatility is of great importance in financial engineering.
“…ARMA models are used to model the conditional expectation of a process given the past, but in an ARMA model the conditional variance given the past is constant. What does this mean for, say, modeling stock returns? Suppose we have noticed that recent daily returns have been unusually volatile. We might expect that tomorrow’s return is also more variable than usual. However, an ARMA model cannot capture this type of behavior because its conditional variance is constant. So we need better time series models if we want to model the nonconstant volatility. In this chapter we look at GARCH time series models that are becoming widely used in econometrics and finance because they have randomly varying volatility.”
Full article (PDF): Link