Under the Avellaneda-Stoikov model the reservation price is r = s - q*gamma*sigma^2*(T-t). The mid is 100.00, you are long 20 lots, gamma = 0.1, sigma = 0.5 per unit time and one unit of time remains. Where do you centre a 1.00 wide quote?

Under the Avellaneda-Stoikov model the reservation price is r = s - q*gamma*sigma^2*(T-t). The mid is 100.00, you are long 20 lots, gamma = 0.1, sigma = 0.5 per unit time and one unit of time remains. Where do you centre a 1.00 wide quote?

Approach: Compute the inventory shift from the reservation price formula, then place the two quotes symmetrically around the reservation price instead of around the market mid.

99.50. That is the reservation price, so the quote is 99.00 bid at 100.00 offer. The inventory shift is q*gamma*sigma^2*(T-t) = 20 * 0.1 * 0.25 * 1 = 0.50, giving 100.00 - 0.50 = 99.50. Centring a 1.00 wide quote there puts the offer at the market mid and the bid a full 1.00 below it, which is the quote skew the Avellaneda-Stoikov model prescribes: holding 20 lots makes you value the asset below the market's mid, so you sell at the mid and buy only at a discount. The shift is linear in inventory and scales with sigma^2 and with the time left, because inventory risk is the variance you still have to carry to the horizon.

Follow-up: How does the optimal half spread change if the order arrival intensity parameter k doubles?

Key concepts: reservation price, inventory risk, quote skew, Avellaneda-Stoikov.