Struct AvellanedaStoikov 

pub struct AvellanedaStoikov {
    pub gamma: f64,
    pub sigma: f64,
    pub kappa: f64,
    pub a: f64,
}

The classic Avellaneda-Stoikov market making model.

Models a market maker optimizing bid/ask quotes to maximize utility of terminal wealth while penalizing inventory risk.

Dynamics

• Price: $dS_t = \sigma dW_t$
• Inventory: $dq_t = dN^{buy}_t - dN^{sell}_t$
• Cash: $dX_t = (S_t + \delta_a) dN^{sell}_t - (S_t - \delta_b) dN^{buy}_t$

Fields

gamma: f64

Risk aversion parameter ($\gamma$). Controls the penalty for holding inventory.

sigma: f64

Volatility of the mid-price ($\sigma$).

kappa: f64

Order filling probability parameter ($\kappa$). Intensity decay rate.

a: f64

Base order arrival intensity ($A$).

Implementations

impl AvellanedaStoikov

pub fn get_spreads(&self, grads: &Gradients<2>) -> (f64, f64)

Computes the optimal bid/ask spreads based on current value function gradients.

formula

$$ \delta^* = \frac{1}{\gamma} \ln(1 + \frac{\gamma}{\kappa}) \pm \frac{\partial V}{\partial q} $$

Trait Implementations

impl Clone for AvellanedaStoikov

fn clone(&self) -> AvellanedaStoikov

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Model<2> for AvellanedaStoikov

type Process = ()

The underlying stochastic process driving the continuous state dimensions. Set to () for models without a corresponding market_model process.

fn process(&self)

Returns the underlying stochastic process, if any.

fn optimize(&self, state: &[f64; 2], grads: &Gradients<2>) -> ControlOutput<2>

Given the current state and value function gradients ($\nabla V$), computations the optimal controls.

fn terminal(&self, _state: &[f64; 2]) -> f64

Computes the terminal value function $V(T, x)$ (Final Condition). Usually represents liquidation cost or final utility of wealth.

fn constant_discount_rate(&self) -> Option<f64>

Optimization hint: Returns Some(r) if the discount rate is constant across all states. Returns None if it depends on state. Default implementation returns None (safe fallback).

fn next_step( &self, current_state: &[f64; 2], dt: f64, noise: &[f64; 2], ) -> [f64; 2]

Simulates the next state for BSDE exploration. Default implementation is a simple random walk: x’ = x + sqrt(dt) * noise

fn next_step_controlled( &self, current_state: &[f64; 2], control: &ControlOutput<2>, dt: f64, noise: &[f64; 2], ) -> [f64; 2]

Simulates the next state for Coupled FBSDE exploration where dynamics depend on control. Default implementation falls back to next_step (Decoupled).

fn is_diffusion_dimension(&self, dim: usize) -> bool

Indicates if a dimension is driven by Brownian diffusion. If true, the BSDE backward step will skip the lambda_plus/minus drift term for this dimension (it is already handled by the forward simulation noise).

fn is_integer_dimension(&self, dim: usize) -> bool

Indicates if a dimension takes only integer values (e.g. inventory q). Controls BSDE initialization: integer dimensions are sampled discretely while continuous dimensions (even if non-diffusion) are sampled with uniform noise. Default: false (continuous).

fn fill_rate_base(&self, _state: &[f64; 2]) -> f64

Base order arrival rate $A$ used for intensity-to-spread conversion. May depend on the current state (e.g. Hawkes lambda). Defaults to 1.0.

fn fill_rate_decay(&self) -> f64

Order fill decay parameter $\kappa$ used for intensity-to-spread conversion. Defaults to 1.0 for non-market-making models. Override in market-making models.

fn discount_rate(&self, _state: &[f64; N]) -> f64

Optional discount rate at the given state. Default implementation returns 0.0.

fn apply_constraint(&self, _state: &[f64; N], value: f64) -> f64

Optional constraint application (e.g. for American options) Default implementation does nothing.

fn transform_noise(&self, _state: &[f64; N], noise: &[f64; N]) -> [f64; N]

Optional transform for standard normal samples before forward stepping.

fn gradient_step(&self, _dim: usize) -> f64

Physical finite-difference step for each state dimension used by BSDE gradient stencils.