Market microstructure

A stock is quoted bid 49.95, ask 50.05. What is the spread in basis points of the mid?

Who pays the spread on a trade?

A maker sells 500 shares at 40.03 and later buys 500 back at 40.07, in USD. What is the result of the round trip?

Two buy orders make up the best bid, both at 99.97: 500 shares entered at 09:30:01 and 2,000 shares entered at 09:30:05. A market sell of 600 shares arrives. Who is filled?

The asks are 50.00 for 200 shares and 50.01 for 300 shares. A market buy of 400 shares arrives. What is its average price in USD?

In a book with the same depth at every level, a market buy of size Q walks the book and costs C against the mid, ignoring the spread. Roughly what does a market buy of size 2Q cost?

Two buy limit orders rest at 99.97. Which one fills first when a market sell order arrives?

900 shares are ahead of your order. Sell volume hits the bid at 250 shares per minute and cancellations ahead remove 50 shares per minute. What is the expected wait in minutes?

You cancel a resting buy order and enter it again at the same price. Where does the new order join the queue?

The average 10-second markout of a maker's buys is −0.8¢. What does that tell you?

With a zero spread, an informed customer expects the value to move by a normal amount with standard deviation $s = 2.5$¢. What is the maker's expected loss on its buy side, in cents?

All customers are noise traders and the fill probability is $e^{-k\delta}$ with $k = 0.4$ per cent. Which half-spread, in cents, maximises the maker's income?

The informed share is $\pi = 0.5$ and the belief is $\mu = 0.5$. What is the ask?

Set $\pi = 0$, so nobody is informed. What happens to the spread?

The informed share rises from $\pi = 0.1$ to $\pi = 0.3$. Roughly how many times faster does the belief learn, using the gain $2\pi^2$ per trade?

The sample covariance of successive price changes is −0.0009 (in USD²). What spread in USD does Roll's estimator give?

Traders become better informed, so the share α of the spread that is information rises. What happens to Roll's estimate?

In a one-auction Kyle market $\sigma_v = 2$ USD and noise trading has standard deviation $\sigma_u = 500$ shares. What is $\lambda$ in USD per share?

The standard deviation of noise trading doubles and nothing else changes. The insider's expected profit…

With one constant $\lambda = 0.002$ USD per share, three auctions left and a gap $V - p = 6$ USD, how many shares does the insider buy in this auction?

A stock has 1.5% daily volatility. An order is 4% of the average daily volume. With $Y = 1$, what price impact does the square-root rule give, in per cent?

A trader who does not care about risk ($\lambda_{\text{risk}} = 0$) faces linear impact. How should the order be split?

The market becomes more volatile while the temporary impact stays the same. How does the optimal schedule change?

A maker is short 1,000 shares. The mid moves with $\sigma = 0.01$ USD per $\sqrt{\text{second}}$. What is the standard deviation of the position's P&L over 100 seconds, in USD?

The maker is long and wants to reduce its inventory using only its quotes. It should

A maker is long 2,000 shares. The half-spread is 0.01 USD and the fee is 0.002 USD per share. What does it cost to flatten the position at the bid, in USD?

A maker is short 4 shares ($q = -4$). The mid is 50, $\gamma = 0.2$, $\sigma = 1$ and $T - t = 0.25$. What is its reservation price?

At the close ($T - t \to 0$), how does a more risk-averse maker's spread compare with a less risk-averse one's?

The maker sells 200 shares at 50.03 when the mid price is 50.00. What is the spread capture in USD?

A maker's spread capture is +500 USD a day, but its adverse selection is −650 USD. What is the first thing to try?