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, derivs: &StateDerivatives<2>) -> (f64, f64)

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

formula

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

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

The base arrival intensity used for intensity-to-spread conversion.

pub fn fill_rate_decay(&self) -> f64

The fill-rate decay parameter used for intensity-to-spread conversion.

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 ControlProblem<2> for AvellanedaStoikov

type Control = MarketMakingControl

The action type. For Merton this is a scalar portfolio fraction; for market making it is a pair of bid/ask intensities.

fn optimize( &self, _t: f64, _state: &[f64; 2], derivs: &StateDerivatives<2>, ) -> Self::Control

Returns the control that maximizes the driver at (t, state).

fn running_reward( &self, _t: f64, _state: &[f64; 2], control: &Self::Control, ) -> f64

Returns the running reward f(t,x,u).

fn bsde_driver( &self, t: f64, state: &[f64; 2], control: &Self::Control, derivs: &StateDerivatives<2>, _dt: f64, ) -> f64

Returns the backward driver consumed by the BSDE regression solver.

fn generator( &self, _t: f64, state: &[f64; 2], _control: &Self::Control, _derivs: &StateDerivatives<2>, ) -> f64

Returns the infinitesimal generator L^u V for the given control and derivative bundle.

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

Terminal value g(x) at the horizon.

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

Discount rate r(t,x). Defaults to zero.

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

Constant discount rate hint. Defaults to None (state dependent).

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

Advances the state one step under the optimal control at forward time t.

fn is_reduced_value(&self) -> bool

Whether the value this problem solves is a reduced value.

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

Whether a dimension is driven by Brownian diffusion.

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

Physical finite-difference step for a dimension, used by mesh-free gradient stencils.

fn driver( &self, t: f64, state: &[f64; N], control: &Self::Control, derivs: &StateDerivatives<N>, ) -> f64

Returns the full HJB driver f(t,x,u) + L^u V.

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

Optional pointwise constraint on the value, e.g. the early-exercise obstacle V >= payoff for an American option.

fn next_step_controlled( &self, t: f64, state: &[f64; N], _control: &Self::Control, dt: f64, noise: &[f64; N], ) -> [f64; N]

Advances the state one step under an explicitly supplied control.

impl EllipticControlProblem<2> for AvellanedaStoikov

fn dimension_kind(&self, dim: usize) -> DimensionKind

Discretization kind for dim.

fn transport( &self, state: &[f64; 2], control: &Self::Control, derivs: &StateDerivatives<2>, ) -> Transport<2>

Transport coefficients and residual source for the given control and derivatives.

fn boundary_conditions(&self) -> BoundaryConditions<N>

Boundary conditions for each dimension.

impl PdeProblem<2> for AvellanedaStoikov

fn dimension_kind(&self, dim: usize) -> DimensionKind

Discretization kind for dim.

fn transport( &self, _t: f64, state: &[f64; 2], control: &Self::Control, derivs: &StateDerivatives<2>, ) -> Transport<2>

Transport and local source for the given control and derivatives.

fn jump_kernel( &self, _t: f64, _state: &[f64; N], _control: &Self::Control, _derivs: &StateDerivatives<N>, transport: &Transport<N>, ) -> JumpKernel<N>

Jump kernel for arbitrary-amplitude jump dimensions.