Avellaneda–Stoikov Reserve Prices and Inventory Skew

Summary

The document presents reserve price and reserve bid and ask expressions from the Avellaneda–Stoikov market-making strategy. The reserve price shifts from the market midpoint according to the trader’s inventory, risk aversion, price volatility, and remaining horizon. The bid and ask quotes also include a spread term involving risk aversion and the order-arrival parameter, so they need not be centered symmetrically on the current midpoint when inventory affects the reservation value.

The author asks why the reserve quotes can intersect the midpoint while describing price moves as discrete steps around the initial value. No answer, derivation, or simulated example is provided. The equations are stated without discussing assumptions behind the model or how parameters should be estimated, so the post introduces the inventory-skew mechanism but leaves the crossing question unresolved.

Key ideas

• Inventory shifts the reserve price relative to the market midpoint.
• Risk aversion, volatility, and time horizon affect the inventory-related price adjustment.
• The bid and ask expressions include a spread term tied to risk aversion and order arrivals.
• The post asks about quote crossings but does not resolve the issue or provide an example.

Tags

# Parameters of Avellaneda-Stoikov inventory strategy


# Parameters of Avellaneda-Stoikov inventory strategy












Consider the reserve price from the algorithm: $$ r(s, t) = s - q\gamma \sigma^2(T-t) $$ where $s$ is the initial value of mid-price on the market, $q$ is a number of stocks that trader has, $\gamma$ is a risk aversion parameter, $T$ is time till trader holds his assets. Also consider reserve bid and ask prices, which equals to: $$ r^{ask} = s + \frac{\gamma \sigma^2 (T-t) + \frac{2}{\gamma}ln(1+\frac{\gamma}{k})}{2}\\ r^{bid} = s - \frac{\gamma \sigma^2 (T-t) + \frac{2}{\gamma}ln(1+\frac{\gamma}{k})}{2} $$

i found out, that reserve bid, ask prices could intersect the mid price, but i don't understand why it happens? Mid price moves up or down with probability $\pm\sigma\sqrt{dt}$ respectively starting from $s$ value, $dt$ is a step. Could anybody help to understand, why such situation happens?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.