Adapting Avellaneda–Stoikov Quotes for Perpetual Futures Funding
Summary
The document outlines an Avellaneda–Stoikov market-making setup for perpetual futures. It gives a reservation price adjusted for inventory, volatility, time remaining, and an expected funding payment, then places bid and ask quotes symmetrically around that reservation price using a spread that depends on risk aversion and order-book depth. The funding adjustment is expressed using the position, expected funding rate, time until funding, and funding interval.
It raises questions rather than resolving them: whether the formulas are correctly derived for perpetuals, how to interpret remaining time without a fixed horizon, and what further changes perpetual markets may require. No derivation, empirical test, or definitive treatment of those questions is included, so the formulas should be read as a proposed setup for review rather than validated guidance. The document also does not discuss how funding forecasts, changing inventory, or market conditions affect the adjustment over time.
Key ideas
- The proposed reservation price shifts with inventory, volatility, remaining time, and an expected funding adjustment.
- The optimal spread combines a risk-related term with a liquidity adjustment based on order-book depth.
- Bid and ask quotes are placed on either side of the reservation price.
- The document leaves the validity of these adjustments for perpetual futures as an open question.
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# Verification of Reservation Price and Optimal Bid/Ask Calculations in Avellaneda-Stoikov Model for Perpetual Futures
# Verification of Reservation Price and Optimal Bid/Ask Calculations in Avellaneda-Stoikov Model for Perpetual Futures
#### Background:
I am implementing an algorithmic market-making strategy based on the Avellaneda-Stoikov model, specifically tailored for perpetual futures, and I have some questions regarding the model adjustments I made for working with perpetual futures.
#### Key Variables and Parameters:
- S: Current mid-price of the asset.
- q: Current inventory position (positive for long, negative for short).
- σ: Volatility of the asset price, estimated using a rolling window of price data.
- γ: Risk aversion coefficient.
- α: Order arrival rate, estimated from market data.
- κ: Order book depth parameter, estimated from market data.
- τ: Fraction of time remaining in the trading period.
- δ: Expected funding payment adjustment.
#### Reservation Price (r):
r = S − qγστ − δ
- Funding payment adjustment: Accounts for the expected funding costs or payments in perpetual futures. Calculated as: $$\delta = q \cdot r_f \cdot \left(\frac{t_f}{T_f}\right)$$, where $r_f$ is the expected funding rate, $t_f$ is the time until funding and $T_f$ is the funding interval.
#### Optimal Spread ( $s^*$ ):
The optimal spread balances the trade-off between profit per trade and the probability of execution:
$$s^* = \gamma\sigma\tau + \frac{2}{\gamma}\ln\left(1 + \frac{\gamma}{\kappa}\right)$$
- First Term ($\gamma\sigma\tau$): Increases the spread with greater risk aversion, volatility, or remaining time.
- Second Term ($\frac{2}{\gamma}\ln\left(1 + \frac{\gamma}{\kappa}\right)$): Adjusts for market liquidity through $\kappa$.
#### Optimal Bid and Ask Prices ( $p_b$ and $p_a$ ):
Positioned around the reservation price:
$$p_b = r - \frac{s^*}{2}$$
$$p_a = r + \frac{s^*}{2}$$
#### Questions:
- Are the above formulas for the reservation price and optimal spread correctly derived and applied in the context of the Avellaneda-Stoikov model? Specifically, does the inclusion of the funding payment adjustment (δ) correctly modify the reservation price for perpetual futures?
- In the case of a perpetual (infinite) trading horizon, is it appropriate to set the time left fraction (𝜏) to 1? If not, how should 𝜏 be adjusted or interpreted when the strategy does not have a fixed end time?
- Are there additional considerations or modifications needed when applying the Avellaneda-Stoikov model to perpetual futures markets as opposed to spot markets?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.