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Trading Rules Over Fundamentals: A Stock Price Formula for High Frequency Trading, Bubbles and Crashes

G. Cadogan

posted on 03 January 2012

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In this paper we present a simple closed form stock price formula, which captures empirical regularities of high frequency trading (HFT), based on two factors: (1) exposure to hedge factor; and (2) hedge factor volatility. Thus, the parsimonious formula is not based on fundamental valuation. For instance, it allows us to use exposure to and volatility of E-mini contracts to predict movements in an underlying index. For application, we first show that for given exposure to hedge factor, and suitable specification of hedge factor volatility, HFT stock price has a closed form double exponential representation. There, in periods of uncertainty, if volatility is above historic average, a relatively small short selling trade strategy is magnified exponentially, and the stock price plummets when strategies are phased locked. Second, we demonstrate how asymmetric response to news is incorporated in the stock price by and through an endogenous EGARCH type volatility process; and find that intraday returns have a U-shaped pattern inherited from HFT strategies. Third, we show that the stock price is bounded from below (crash), i.e. flight to quality, but not from above (bubble), i.e. confidence, when phased locked trade strategies violate prerequisites of van der Corput's Lemma. Thus, extant regulatory proposals to control price dynamics of select stocks, i.e., ''limit up/limit down" bands over 5-minute rolling windows, may mitigate but not stop future market crashes or price bubbles from manifesting in underlying indexes that exhibit HFT stock price dynamics.