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, derivs: &StateDerivatives<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.

pub 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.

pub fn fill_rate_decay(&self) -> f64

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

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 ControlProblem<3> for HestonHawkes

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; 3], derivs: &StateDerivatives<3>, ) -> Self::Control

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

fn running_reward( &self, _t: f64, _state: &[f64; 3], control: &Self::Control, ) -> f64

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

fn bsde_driver( &self, _t: f64, state: &[f64; 3], control: &Self::Control, _derivs: &StateDerivatives<3>, dt: f64, ) -> f64

Returns the backward driver consumed by the BSDE regression solver.

fn generator( &self, _t: f64, state: &[f64; 3], _control: &Self::Control, derivs: &StateDerivatives<3>, ) -> f64

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

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

Terminal value g(x) at the horizon.

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

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

fn next_step_controlled( &self, _t: f64, state: &[f64; 3], control: &Self::Control, dt: f64, noise: &[f64; 3], ) -> [f64; 3]

Advances the state one step under an explicitly supplied control.

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 is_reduced_value(&self) -> bool

Whether the value this problem solves is a reduced value.

impl Debug for HestonHawkes

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

Formats the value using the given formatter.

impl PdeProblem<3> for HestonHawkes

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

Discretization kind for dim.

fn transport( &self, _t: f64, state: &[f64; 3], control: &Self::Control, derivs: &StateDerivatives<3>, ) -> Transport<3>

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.