# Development in Intraday Volatility Forecasting

One of my cur­rent inter­est in microstruc­ture research is to under­stand what dri­ves intra­day volatil­ity in stock prices. Why? From an eco­nomic point of view, it is not so obvi­ous why intra­day volatil­ity mat­ters beside relat­ing intra­day volatil­ity to infor­ma­tion arrival. But from a prac­ti­cal point of view, it mat­ters. Take for exam­ple a tran­si­tion port­fo­lio man­ager that has for objec­tive to lower its trans­ac­tion cost. If price volatil­ity is high, we then expect a volatile bid-ask spread and mar­ket depth, which in turn increase trans­ac­tion cost. For this blog post, I sim­ply want to high­light a new research by Cont et al. (2014) in the Jour­nal of Finan­cial Econo­met­rics that attempts to mea­sure intra­day volatil­ity in a very clever way. But first, let me intro­duce you to the VPIN mea­sure devel­oped by Easley, Lopez de Prado and O’hara to fore­cast intra­day volatility.

The recent aca­d­e­mic arti­cle by Easley, Lopez de Prado and O’hara (2013) show that mar­ket order imbal­ance can antic­i­pate moments of intra­day tur­bu­lence in stock prices if we “deform” cal­en­dar time and com­pute the mar­ket order imbal­ance in vol­ume time. By deform­ing cal­en­dar time, it means to move away from reg­u­lar time tick like one minute or sec­ond time inter­val. Easley et al. (2012) sug­gest a volume-clock where the time inter­val length will be a func­tion of the trad­ing vol­ume activ­ity. Let say we start our trad­ing day at 9:30am and there is a high amount of vol­ume at the open­ing of the mar­ket then we can set our first time inter­val from 9:30:00 to 9:30:44 and the next one from 9:30:44 to 9:30:54 if vol­ume increases. If the amount of trad­ing vol­ume decreases from our last inter­val, then the end of the next inter­val may be at 9:33am and hence longer. For each of these inter­vals we com­pute the mar­ket order imbal­ance. The authors then sug­gest to sum the absolute value of the mar­ket order imbal­ance over mul­ti­ple inter­vals. Higher is the sum of order imbal­ance, higher the like­li­hood of high mar­ket volatil­ity. I have skipped a lot of details on the mea­sure but you get the essence.

Fol­low­ing the series of paper on the VPIN by Easley et al., Bon­darenko and Boller­slev (2013) pub­lished a paper in the Jour­nal of Finan­cial Mar­kets rebut­ting the abil­ity of the VPIN to antic­i­pate mar­ket volatil­ity. I won’t go much in the details, but it is worth the read. The debate between Easley et al. and Bodarenko and Boller­slev con­tin­ues here and here.

Then this brings the work of Cont et al. (2014). The author sug­gest a very clever way to “poten­tially” fore­cast intra­day volatil­ity. They don’t fore­cast volatil­ity per se but show that there is a high cor­re­la­tion between their mea­sure of order flow imbal­ance and mar­ket volatil­ity (or price changes). What I like about their mea­sure is that they com­bine both mar­ket order imbal­ance and liq­uid­ity pro­vi­sion imbal­ance. It is com­puted as follow:

$L_k^b-C_k^b+M_k^b-L_k^s+C_k^s-M_k^s$ where $L$ , $C$ , and $M$ stands for a limit order, can­cel of an order, and mar­ket order exe­cu­tion of a $k$ order on the buy $b$ or sell $s$ side of the book.

As you can see, they incor­po­rate both the the imbal­ance of the mar­ket and limit side. They argue that when the limit order imbal­ance $L_k^b-C_k^b-L_k^s+C_k^s$ is high, the mar­ket order imbal­ance $M_k^b-M_k^s$ impact on stock prices becomes very noisy. How liq­uid­ity is pro­vided in mar­kets mat­ters to fore­cast and antic­i­pate mar­ket intra­day volatil­ity. It may actu­ally be more impor­tant than mar­ket order imbal­ance sim­ply because it is liq­uid­ity providers that set prices afterall.

What is yet to be done is to use their mea­sure to fore­cast volatil­ity both in cal­en­dar and vol­ume time… which I hope to take the time and test it out.