Put a number on your reservation price

Question

The mid-market fair value is s = 100. You are currently long q = 5 units. Your risk aversion is \gamma = 0.1 and the per-unit price variance over your horizon is \sigma^2 = 4. Where should you center your quotes (your reservation price), and which way does that push your bid and offer?

Accepted Answer

Your reservation price is the fair value adjusted for the inventory you are carrying: r = s - q\,\gamma\,\sigma^2. Being long (q 0) makes you value the asset a little less than the market, because you would rather offload than accumulate, so your indifference price sits below the mid. Plugging in: r = 100 - (5)(0.1)(4) = 100 - 2 = 98. Center your quotes at 98, not 100. With a two-unit-wide half-spread you would show roughly 97 bid, 99 offer. Both quotes sit two points below the fair mid, which is exactly what a long position calls for: - Your offer at 99 is below fair, so it is more likely to…

Put a number on your reservation price

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