hard · Market Microstructure
A dealer in 'Beta' stock manages inventory with a risk aversion parameter γ = 0.02. The stock's variance is 1.0 and the dealer is currently long q = +500 shares.
If the symmetric half-spread is $0.25 and the remaining time horizon (T - t) is 0.01 days, how should the dealer shift their quotes relative to the $100.00 midpoint?
- Shift the bid up to $100.00 and leave the ask at $100.25.
- Shift the midpoint up to $100.10, quoting $99.85 / $100.35.
- Shift the midpoint down to $99.90, quoting $99.65 / $100.15.
- Widen the spread to $0.60 without shifting the midpoint.
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