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# Calculating fair value of stock prices of a pairs trading strategy in high frequency?

Discussion in 'Trading' started by tradingbuddha, Aug 18, 2011.

1. ### tradingbuddha

Iâm working on an Electronic arbitrage system that looks for cases at one particular moment, where some security is mispriced relative to some other security (i.e., in violation of the law of one price). The goal of the predictor strategy is to identify price discrepancies that involve a time component. In essence, the predictor combs through market data looking for cases where he can assert that a security trading at price Y will move over time to a higher price Z with enough certainty that he is willing to buy at Y with plans to sell when it gets to Z. Or that it will move from Y down to X so he is willing to short it at Y and buy it back at X to close out the short. The length of the time component here can vary wildly. Because our interest is in high- frequency trading, we will focus on strategies intended to exploit changes expected to play out in at most seconds or minutes.

Here, one of a pair of stocks that typically move in concert with each other is identified as a laggardâit has not yet changed the way it is expected to, relative to the other. The predictor expects it to catch up (or down) with the leader eventually. But until it does, the predictor considers it mispriced. In statistical arbitrage terms, it is said to have, during this time period, alpha. Alpha is a measure of excess return, and itâs widely used by predictors to quantify a mispricing. A vague assertion like âthat stock is underpriced,â no matter how true, does no good here. We need to know precisely, in pennies or fraction of pennies, exactly how much the stock is underpriced because I will be delegating the actual work here to computers that require specific instructions. Once so-called alpha signals are detected (say, in a pairs laggard) and alpha is calculated, it is often expressed in terms of a fair value. This is the price the predictor is confident is the perfectly fair one, the price at which neither side of a trade will profit. For example, the fair price of MSFT may be, at some particular instant, \$30.4971. Should it later be identified as a pairs laggard (say, to GOOG), its alpha might increase, bumping the fair value to something like \$30.5112. How is fair value used? Since all high frequency trading opportunities are identified in one place and one place only: the order book. The predictor has his eyesâweâll call it electronic arbitrageurâfocused on bids and offers as they change. He looks for bids that are too high and offers that are too low, according to her alpha strategy. He requires, of course, some price with which to compare those bids and offers to decide what bids to hit and what offers to lift. That price is the fair value, and it reduces the predictorâs job at the order book to two basic rules. If a bid price is above the fair value, hit it. If an offer price is below the fair value, lift it. There are likely to be other subtleties, such as how much a bid or price has to cross the fair value, and the predictor applies it not only when bids and offers change but also when his fair value changes. But still, compared with so much else in finance, this should be trivial task indeed. And this is the beauty of the fair value approach, the way it would make the electronic arbitrageursâ jobâits algorithmâvery simple. And simple algorithms are great because they allow the programmer to write extremely efficient code, code that can get the job done very quickly.

How would I theoretically calculate a fair value of such a pairs trading strategy if I wish to execute this type of strategy in a high frequency setting or what are the exact step by step techniques or a model to calculate a fair value and execute this type of strategy. Is there any third party software that can help me execute this type of strategy in live market? Sorry for posting so many questions and thanks in advance.

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