All right. Let's first talk about what type of data is available within order driven market. First, there are two types of data in such markets, transaction data and quotes data. First, let me start with transaction data. Transaction data simply provides a record of traded quantities or fall assets along with actual execution prices. So, this is really the same as the conventional financial data as we defined or used so far. But there is also one more type of data that we did not encounter so far and this is called a quotes data. So, what are quotes? Quotes are proposals to buy or sell a certain quantity of an asset at a given pre-specified price. Now, when we add quotes to actual trade prices or we get not just a single payer over price and amount traded, but instead we have a number of such pairs over price and the quantity. Now, let's talk a bit more in details about each type of this data. First, let's talk about transaction data. So, transaction data are data that describe actual trades. Every trade has three characteristics; a time stamp, price, and the quantity traded. Now, this is quite different from many financial time series models. This model usually assume a setting with a discrete equally spaced timesteps, but such regular timesteps, for example daily, will only arise after we aggregate all traits within one day. If we look at things at the timescale over seconds or LOB, times between trades appear quite irregular. In this setting, durations between trades become functions of the price and the state of the limit order book. The next difference is that the price changes are now discrete, they are given by a multiple of a tick, which is a minimal step for a stock price that it can move. In the US markets, one tick equals one cent. So, this means among other things that the price changes are not independent but rather autocorrelated in the short-term but this autocorrelations quickly decay with time. In addition, there are also strong autocorrelation seen trading volumes. So in the LOB, trades happen irregularly in time. Moreover, durations between trades depend on the state of the LOB. Because of all these new complexities, it seems that the regular time series formulation with a discrete-time grid is not adequate here. Instead, a continuous-time formulation of dynamics might be preferred. Also, intraday data exhibit a strong seasonality. In particular, there's usually lots of activity when a market opens or near when it closes. Normally, there's less activity closer to noon. Therefore, intraday data should be seasoned before it can be used. Next, let's discuss types of orders that exist in electronic markets. There are two types of orders, market orders and limit orders. Let's start with market orders. This is how they work. Market order is an order for a dealer to buy or sell a given quantity X of a stock, such orders are executed immediately by the exchange via their specialists. On the other hand, limit orders are quite different. They are orders to buy or sell a given amount X, but for a quoted price. If the desired prices below the current bid-ask spread, such order will not be executed but instead will be put in the queue, as we will discuss in more details shortly. So, all incoming limit orders at each price level are summarized as the total number of orders at each price level, and this summary is called the Limit Order Book or the LOB for short. Such aggregation is done separately on the buy side and the sell side. The highest price on the buy side is called the bid price and the lowest price on the sell side is called the ask price. When a limit order arrives, it seats in the LOB until it's matched by an incoming market order on the opposite side of the LOB. Alternatively, it may not wait until then and get cancelled at anytime before. Now, the availability of quotes at different price levels leads to new types of data. First, we have the so-called quote data, sometimes also called the Level-I order book data. This data simply collects bid and ask prices and the corresponding quantities quoted. So, it only looks at the highest segments on each side of the LOB. There is also a more detailed Level-II order book data, which contains information about prices and quantities of five highest levels of the LOB. These data are obviously much richer than quote data but it's also more expensive and takes more storage. In addition to limit orders, there are also market orders. As we already said, the market order is simply an order to buy or sell a given quantity X at the best price possible. Finally, for this video, I wanted to briefly talk about how trades and quote data can be used together. First, about data sources. There are a number of providers of such types of data. One of the best known examples is the TAQ data base provided by New York Stock Exchange. Now, when you have both the trading and quotes data, you can use them in multiple ways. One interesting application is to use them to reconstruct the sequence of market and limit orders. We can also use such algorithms to infer whether a given transaction was initiated by a buy or sell side. The method is essentially based on comparison between the trade price and the most recent bid-ask quote. You can read about details of such approaches in the paper that I cited on the slide.
