1. The Flaw of Constant Risk Aversion

In the standard Avellaneda-Stoikov framework, the risk aversion parameter \(\gamma\) is a static input chosen by the trader. This implies that the market maker has the same tolerance for risk at all times.

This is patently false. A rational agent's appetite for risk changes based on their environment.

In a calm, low-volatility market, risk appetite is high. The market maker should use a low \(\gamma\), leading to tighter spreads and a greater willingness to hold inventory to capture those spreads.
In a chaotic, high-volatility market (e.g., during a major hack or regulatory announcement), risk appetite is low. The market maker should use a high \(\gamma\), leading to wider spreads and an urgent need to flatten inventory.

Treating \(\gamma\) as a constant leads to a strategy that is too timid in calm markets and far too reckless in volatile ones.

2. Building a Dynamic \(\gamma\) Model

At introdeus.xyz, our \(\gamma\) is not a single number; it's a dynamic function that updates in real-time.

\(\gamma_t = f(V_t, I_t, C_t, ...)\)

Where the inputs are a vector of real-time market features:

\(V_t\): Volatility. The most important input. We use a blend of short-term realized volatility and implied volatility from options markets (e.g., the VIX or DVOL indices). As volatility spikes, \(\gamma_t\) increases quadratically.
\(I_t\): Inventory. The function is also dependent on our current inventory. The risk of adding one more unit of a token is much higher if we already hold a large position. Our \(\gamma_t\) increases as the absolute value of our inventory, \(|q_t|\), increases.
\(C_t\): Correlation. We analyze the correlation matrix of the entire crypto market. If we observe a "risk-off" event where all assets become highly correlated (i.e., they all start moving down together), this indicates systemic risk. In this scenario, \(\gamma_t\) for all assets is increased significantly, as the benefits of diversification have vanished.

3. A Concrete Functional Form

A simplified version of our dynamic risk aversion function might look like this:

\(\gamma_t = \gamma_{base} + c_1 \cdot \hat{\sigma_t}^2 + c_2 \cdot q_t^2 + c_3 \cdot \rho_t^{market}\)

Where:

\(\gamma_{base}\): A baseline risk aversion level.
\(\hat{\sigma_t}^2\): The current estimate of market variance.
\(q_t^2\): The square of the current inventory, capturing the quadratic nature of inventory risk.
\(\rho_t^{market}\): A measure of the average correlation in the market.
\(c_1, c_2, c_3\): Coefficients that determine the sensitivity to each factor. These are calibrated via historical backtesting.

The Feedback Loop

This dynamic \(\gamma_t\) creates a crucial feedback loop for risk management:

Market volatility (\(\hat{\sigma_t}\)) increases.
\(\gamma_t\) increases automatically.
The optimal spread (which is proportional to \(\gamma_t\)) widens.
The reservation price skew becomes more aggressive (also proportional to \(\gamma_t\)).
The market maker is now quoting wider and is more aggressively trying to offload inventory.
This naturally reduces the risk of the strategy exactly when the market becomes more dangerous.

A static \(\gamma\) model lacks this essential, self-correcting risk mechanism.

4. Conclusion: From Parameter to "Fear Index"

By modeling risk aversion dynamically, we transform \(\gamma\) from a simple input parameter into a sophisticated, real-time "fear index." It's a quantitative measure of our appetite for risk, which adapts rationally to changing market conditions. This ensures that our strategies remain robust and profitable, not just in average market conditions, but during the periods of extreme stress where most other market makers fail.