In Section 11.2, we describe statistical models and methods to study market microstructure. As pointed out in Section 3.1.2, the highest resolution can be obtained from transaction-by-transaction or trade-by-trade data in securities markets. Statistical learning of market patterns can proceed with different levels of resolution. Hedge funds have now become big users of derivatives for all three purposes, namely hedging, speculation, and arbitrage. However, as pointed out by Hull (2006, Chapter 1), derivatives markets have also attracted speculators and arbitrageurs who try to take advantage of the discrepancies between the arbitrage-free theories and the actual market prices. Since the martingale models preclude making risk-adjusted profits via trading strategies, these theories imply that the derivatives markets would only attract hedgers, who use derivatives to reduce the risk they face from future movements of stock or bond prices. The finance theories underlying Chapters 8 and 10 assume the absence of arbitrage, leading to pricing models that are martingales after adjustments for the market price of risk.
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