Struct Heston 

pub struct Heston {

    pub gamma: f64,
    pub kappa_m: f64,
    pub a: f64,
    pub v_kappa: f64,
    pub v_theta: f64,
    pub v_xi: f64,
    pub rho: f64,
    pub price_scale: f64,
    pub dv: f64,
    pub dq: f64,
    pub q_min: f64,
    pub q_max: f64,
    pub terminal_condition: TerminalCondition,
}

Heston Stochastic Volatility Model for Market Making

Extends the Avellaneda-Stoikov model by adding stochastic volatility to the mid-price. The value function depends on both inventory and current variance.

Dynamics

• $dS_t = S_0 \sqrt{v_t} dW^S_t$
• $dv_t = \kappa_v (\theta - v_t) dt + \xi \sqrt{v_t} dW^v_t$

This reduced HJB model has state [q, v] only (no spot state). To align with a multiplicative market process where price diffusion scales with S_t, we freeze spot at a reference level price_scale (typically initial price).

Fields

gamma: f64

Risk aversion for inventory holding.

kappa_m: f64

Order filling intensity decay ($\kappa$).

a: f64

Base order arrival intensity ($A$).

v_kappa: f64

Mean reversion speed for variance ($\kappa_v$).

v_theta: f64

Long-run mean variance ($\theta$).

v_xi: f64

Volatility of variance (vol-of-vol, $\xi$).

rho: f64

Correlation between price and variance Brownian motions ($\rho$).

price_scale: f64

Reference spot level used to map relative variance into absolute price-risk scale.

dv: f64

Grid step size for the variance dimension.

dq: f64

Grid step for inventory dimension (defaults to 1.0 for integer grid).

q_min: f64

Minimum inventory (lower hard boundary). Defaults to -infinity (no constraint).

q_max: f64

Maximum inventory (upper hard boundary). Defaults to +infinity (no constraint).

terminal_condition: TerminalCondition

Terminal condition for the value function at T. Defaults to Zero.

Implementations

impl Heston

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

pub fn with_terminal_condition( self, terminal_condition: TerminalCondition, ) -> Self

pub fn with_inventory_bounds(self, q_min: f64, q_max: f64) -> Self

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

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

pub fn with_price_scale(self, price_scale: f64) -> Self

pub fn with_dv(self, dv: f64) -> Self

pub fn with_dq(self, dq: f64) -> Self

pub fn with_grid_steps(self, dx: &[f64; 2]) -> Self

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

pub fn get_spreads(&self, derivs: &StateDerivatives<2>) -> (f64, f64)

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 Heston

fn clone(&self) -> Heston

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ControlProblem<2> for Heston

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 next_step_controlled( &self, _t: f64, state: &[f64; 2], control: &Self::Control, dt: f64, noise: &[f64; 2], ) -> [f64; 2]

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 Copy for Heston

impl Debug for Heston

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

Formats the value using the given formatter.

impl PdeProblem<2> for Heston

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.