Struct AmericanPut 

pub struct AmericanPut {
    pub risk_free_rate: f64,
    pub volatility: f64,
    pub strike: f64,
    pub dx: f64,
}

American Put Option

Models the optimal exercise strategy for an American Put option. This is formulated as an optimal stopping problem, but can be solved via HJB by treating the exercise decision as a control.

Dynamics follow Geometric Brownian Motion for the underlying asset.

Fields

risk_free_rate: f64

Risk-free interest rate (r).

volatility: f64

Volatility of the underlying asset ($\sigma$).

strike: f64

Strike price (K).

dx: f64

Spatial discretization step size (dx) used for finite difference coefficients.

Implementations

impl AmericanPut

pub fn new(risk_free_rate: f64, volatility: f64, strike: f64, dx: f64) -> Self

pub fn set_dx(&mut self, dx: f64)

Trait Implementations

impl Model<1> for AmericanPut

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; 1], _grads: &Gradients<1>) -> ControlOutput<1>

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

fn terminal(&self, state: &[f64; 1]) -> f64

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

fn discount_rate(&self, _state: &[f64; 1]) -> f64

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

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 apply_constraint(&self, state: &[f64; 1], value: f64) -> f64

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

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

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; 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 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 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.