How a risk limit reaches into your quotes

Question

Your risk desk caps the one-day 99% Value-at-Risk of any single position at \100{,}000. The stock has daily volatility \sigma = \1.50 per share, and the 99\% one-tailed normal multiplier is 2.33. What maximum inventory does the VaR cap imply? How does that number reach into how you quote and skew?

Accepted Answer

From VaR to a share limit. One-day 99\% VaR of a q-share position is 	ext{VaR} = 2.33 	imes \sigma 	imes q = 2.33 	imes 1.50 	imes q = 3.495\,q. Set it equal to the \100{,}000 cap: 3.495\,q = 100{,}000 \;\Longrightarrow\; q{\max} = \frac{100{,}000}{3.495} \approx 28{,}600 	ext{ shares.} So the VaR limit says: never let inventory exceed about \pm 28{,}600 shares. How the limit reaches into your quotes. The cap isn't just a tripwire at 28{,}600, it shapes your quoting continuously as you approach it: - Near flat, you quote symmetric and tight, harvesting spread on both sides. You have ple…

How a risk limit reaches into your quotes

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