“Listed futures on VIX and its cousins give exposure to implied variance. But getting exposure to realised variance is very different and usually has been the realm of OTC variance swaps. Here we examine strategies to trade the realised variance using only listed instruments, with simple time-independent formulas not requiring models such as Black-Scholes.”

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“We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intraday contributions. We find, as perhaps expected, that the overnight and intraday returns behave completely differently. For example, while past intra-day returns affect equally the future intraday and overnight volatilities, past overnight returns have a weak effect on future intra-day volatilities (except for the very next one) but impact substantially future overnight volatilities. The exogenous component of overnight volatilities is found to be close to zero, which means that the lion’s share of overnight volatility comes from feedback effects. The residual kurtosis of returns is small for intraday returns but infinite for overnight returns. We provide a plausible interpretation for these findings, and show that our Intraday/Overnight model significantly outperforms the standard ARCH framework based on daily returns for Out-of-Sample predictions.”

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“Uncertainty is generally avoided when investing. Volatility is a popular proxy for investment uncertainty, and indeed low volatility stocks outperform high volatility stocks. However, there are also many other possible measures of uncertainty, among which are entropy and the Hurst exponent. Here we show that these measures also predict groups of stocks that outperform.”

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“Once upon a time dispersion trading desks used to be the kings (and queens) of volatility trading in the equity arena (if we ignore the 35 mio USD short vega position by LTCM).

“Dispersion desks can handle significant volatility risks in the same way that a basket desk can handle extremely large deltas per instrument or a cap/floor vs. swaption trader can handle extremely large volatility risks per underlying. As a matter of fact, a dispersion trader is essentially a cap/floor vs. swaptions trader, albeit somewhat less structured. Dispersion traders can come into a single stock and sometimes sell signifcant vegas (read: millions) before anyone knows what is happening.”

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“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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“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.”

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“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. ”

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“…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.”

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“The volatility index, sometimes called by financial professionals and academics as
“the investor gauge of fear” has developed overtime to become one of the highlights
of modern day financial markets. Due to the many financial mishaps during the last
two decades such as LTCM (Long Term Capital Management), the Asian Crisis just
to name a few and also the discovery of the volatility skew, many financial experts
are seeing volatility risk as one of the prime and hidden risk factors on capital
markets. This paper will mainly emphasize on the developments in measuring and
estimating volatility with a concluding analysis of the historical time series of the new
volatility indices at the Deutsche Boerse.”

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“In this paper, we solve the problem of solution of stochastic volatility models in which the volatility diffusion can be solved by a one dimensional Fokker-planck equation. We use one dimensional transition probabilities for the evolution of PDE of variance. We also find dynamics of evolution of expected value of any path dependent function of stochastic volatility variable along the PDE grid. Using this technique, we find the conditional expected values of moments of log of terminal asset price along every node of one dimensional forward Kolmogorov PDE. We use the conditional distribution of moments of above path integrals along the variance grid and use Edgeworth expansions to calculate the density of log of asset price. Main result of the paper gives dynamics of evolution of conditional expected value of a path dependent function of volatility (or any other SDE) at any node on the PDE grid using just one dimensional PDE if we can describe its one step conditional evolution between different nodes of the PDE.”

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