Struct HestonHawkes 

pub struct HestonHawkes {
    pub gamma: f64,
    pub kappa: f64,
    pub v_kappa: f64,
    pub v_theta: f64,
    pub v_xi: f64,
    pub rho: f64,
    pub dv: f64,
    pub alpha: f64,
    pub beta: f64,
    pub mu_lambda: f64,
    pub lambda_step: f64,
    pub dq: f64,
}

Combined Heston-Hawkes Model for Market Making (N=3).

Merges stochastic volatility (Heston) with self-exciting order flow (Hawkes) into a single three-dimensional model, demonstrating seamless N=3 extensibility.

State Space

[q, v, lambda] where:

• q (dim 0): Inventory level (discrete, jump-controlled)
• v (dim 1): Stochastic variance following CIR dynamics
• lambda (dim 2): Hawkes order arrival intensity (mean-reverting with self-excitation)

Dynamics

• Inventory: $dq = +1$ (buy fill) or $-1$ (sell fill)
• Variance: $dv_t = \kappa_v (\theta - v_t) dt + \xi \sqrt{v_t} dW^v_t$
• Intensity: $d\lambda_t = \beta (\mu_\lambda - \lambda_t) dt + \alpha \lambda_t dt$

The optimal spreads incorporate both volatility risk premia (from Heston) and state-dependent arrival rates (from Hawkes).

Fields

gamma: f64

Risk aversion for inventory holding.

kappa: f64

Order filling intensity decay.

v_kappa: f64

Mean reversion speed for variance.

v_theta: f64

Long-run mean variance.

v_xi: f64

Volatility of variance.

rho: f64

Correlation between price and variance Brownian motions ($\rho$). Enters the HJB through the cross-variation drift: $-\gamma \rho \xi v q$.

dv: f64

Grid step size for variance dimension.

alpha: f64

Self-excitation jump size.

beta: f64

Mean-reversion speed of intensity.

mu_lambda: f64

Baseline intensity level.

lambda_step: f64

Grid step for intensity dimension.

dq: f64

Grid step for inventory dimension.

Implementations

impl HestonHawkes

pub fn new(gamma: f64, kappa: f64) -> Self

pub fn with_heston_params(self, v_kappa: f64, v_theta: f64, v_xi: f64) -> Self

pub fn with_rho(self, rho: f64) -> Self

pub fn with_hawkes_params(self, alpha: f64, beta: f64, mu_lambda: f64) -> Self

pub fn with_grid_steps(self, dx: &[f64; 3]) -> Self

Sets grid step sizes from a Grid<3>. Dimension 0 = inventory (dq), Dimension 1 = variance (dv), Dimension 2 = intensity (lambda_step).

pub fn get_spreads(&self, _q: f64, v: f64, grads: &Gradients<3>) -> (f64, f64)

Compute optimal bid/ask spreads given the current state and value gradients.

Combines the Heston volatility risk premium with the Hawkes intensity dependence.

Trait Implementations

impl Clone for HestonHawkes

fn clone(&self) -> HestonHawkes

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HestonHawkes

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Model<3> for HestonHawkes

fn fill_rate_base(&self, state: &[f64; 3]) -> f64

The base arrival intensity is state-dependent: returns the current intensity state[2] (clamped above 0) for intensity-to-spread conversion.

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; 3], grads: &Gradients<3>) -> ControlOutput<3>

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

fn terminal(&self, _state: &[f64; 3]) -> 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; 3], dt: f64, noise: &[f64; 3], ) -> [f64; 3]

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

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 gradient_step(&self, dim: usize) -> f64

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

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 next_step_controlled( &self, current_state: &[f64; N], _control: &ControlOutput<N>, dt: f64, noise: &[f64; N], ) -> [f64; N]

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

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

Optional transform for standard normal samples before forward stepping.