Two desks, same position, who skews harder?

Question

Two desks, A and B, are each long the identical $10{,}000$ shares of the same stock, and both agree fair value is unchanged. Yet desk A skews its quotes down much harder than desk B.

What differences between the two desks would justify A skewing more aggressively? Tie your answer to the reservation-price formula.

Accepted Answer

Inventory q is the same, so the skew gap must come from the other factors in r = 	ext{fair} - q\,\gamma\,\sigma^2 T. The skew is the distance q\,\gamma\,\sigma^2 T from fair, and it grows with each of: - Risk aversion \gamma. Desk A may run a tighter risk budget, be closer to a loss limit, or simply dislike variance more. Higher \gamma means it pays more, in forgone edge, to shed the position, so it skews harder. - Volatility \sigma^2. Even for the same name, A may forecast higher near-term volatility (an event looming, a regime shift), which makes the same 10{,}000 shares riskier to hold, w…

Two desks, same position, who skews harder?

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