Here is a list of Quant Books and Research Papers on Volume-time and Volatility

(Last Updated On: March 28, 2012)

Here is a list of Quant Books and Research Papers on Volume-time and Volatility

Is there an empirical or theoretical study, ideally across different asset classes, of the relationship between s_t, the volatility of a given security at (or around) time t, and v_t, the total $ volume of the given security traded in the market at (or around) time t?

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Here are a few related studies:

• Ané, T., and H. Geman (2000): “Order Flow, Transaction Clock and Normality of Asset Returns”, Journal of Finance, 55: 2259–2284.

• Clark, P. K. (1970): “A Subordinated Stochastic Process Model of Cotton Futures Prices”, unpublished Ph.D. dissertation, Harvard University, May.

• Clark, P. K. (1973): “A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices”, Econometrica, 41 (1): 135-155.

• Mandelbrot, B., and M. Taylor (1967): “On the Distribution of Stock Price Differences”, Operations Research, 15 (6): 1057-1062.

• Mandelbrot, B. (1973): “Comments on ‘A subordinated stochastic process model with finite variance for speculative prices by Peter K. Clark’”, Econometrica, 41 (1): 157-159.

Here is how Mandelbrot and Taylor [1967] saw it:

“Price changes over a fixed number of transactions may have a Gaussian distribution. Price changes over a fixed time period may follow a stable Paretian distribution, whose variance is infinite. Since the number of transactions in any time period is random, the above statements are not necessarily in disagreement. […] Basically, our point is this: the Gaussian random walk as applied to transactions is compatible with a symmetric stable Paretian random walk as applied to fixed time intervals.”

 

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Hiemstra and Jones (Journal of Finance, 1994) did a generalized causality study, T. Andersen (Journal of Finance, 1996) used a microstructure framewok. More recently, Giot and Laurent (Journal of Empirical Finance, 2010) used a realized vol/jump component approach.

 

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it’s not exactly on-point, but might be handy if you’re creating a framework, the author gave the paper at last year’s sofie conference in chicago:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1525410

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Stochastic subordination and time change are classical theoretical machinery, per literature cited by Marcos.

Numerous time / clock formalisms have been proposed and empirical evaluated; for example: Mendelbrot with “trading time”; Dacorogna et al. (2001) with “upsilon time”; and Derman with “intrinsic time” (2002).

Literature on this topic continues to be active; for example, see references in McCulloch (2011).

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Gallant Rossi Tauchen, RFS 1993, volatility and volume for the S&P500

 

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Also: George Tauchen, Harold Zhangb, Ming Liua; Volume, volatility, and leverage: A dynamic analysis; Journal of Econometrics Volume 74, Issue 1, September 1996, Pages 177–208

The paper recommended by Thierry Michel [Trading activity, realized volatility and jumps (Giot, Laurent, Petitjean, 2010, Journal of Empirical Finance 17, 168-175] includes lieterature review and can be found here http://www.core.ucl.ac.be/~laurent/pdf/Petitjean.pdf

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George Tauchen, Harold Zhangb, Ming Liua; Volume, volatility, and leverage: A dynamic analysis; Journal of Econometrics Volume 74, Issue 1, September 1996, Pages 177–208 can be found here:

http://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/1897/Tauchen_volume_volatility_and_leverage.pdf?sequence=1

It uses NONLINEAR, non-parameteric impulse response analysis to investigate the relationship between Volatility, Volume and the Leverage Effect. The nonlinearity is explored through perturbation analysis (so it is dealing with small nonlinearities).

 

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the following are detailed citation for references in above comment:

Dacorogna, Michel et al. (2001), An Introduction to High-Frequency Finance. http://books.google.com/books?id=dobO95EBcqsC

Derman, Emanuel (2002), “The perception of time, risk and return during periods of speculation”. http://www.ederman.com/new/docs/qf-market_bubbles.pdf

Mandelbrot, B. and Taylor, H. (1967), “On the Distribution of Stock Price Differences”, Operations Research 15, 1057-1062. http://www.jstor.org/stable/168611

McCulloch, James (2011), “Fractal Market Time”. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1803888

 

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