Futures Exchange Data Feed Delay
A futures exchange provides two data feeds: a fast direct feed (arriving at time $t$) and a slower consolidated feed (arriving at time $t + \delta$, where $\delta \sim \text{Exp}(\lambda)$ with mean $50$ microseconds).
You observe a price change on the fast feed at time $t_0$.
1. What is the probability the consolidated feed has not yet reflected this change after
00$ microseconds?
2. If you can trade on the consolidated feed's stale price, what is your information advantage as a function of your order latency $\tau$?
3. How does this connect to latency arbitrage in practice, and what does it tell you about the value of speed?
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