Struct MertonJumpDiffusion 

pub struct MertonJumpDiffusion {
    pub initial_price: f64,
    pub mu: f64,
    pub sigma: f64,
    pub lambda: f64,
    pub jump_mean: f64,
    pub jump_std: f64,
}

Merton Jump-Diffusion model

Combines continuous GBM dynamics with discrete jumps to model market crashes and rallies.

Parameters

• mu: Drift rate (expected return excluding jumps)
• sigma: Continuous volatility
• lambda: Jump intensity (expected jumps per year)
• jump_mean: Mean of log jump size
• jump_std: Std of log jump size

Example

use aprender::monte_carlo::prelude::*;

let model = MertonJumpDiffusion::new(100.0, 0.08, 0.15)
    .with_jumps(1.0, -0.1, 0.15);  // 1 jump/year, -10% mean, 15% std

let engine = MonteCarloEngine::reproducible(42).with_n_simulations(1000);
let result = engine.simulate(&model, &TimeHorizon::years(1));

Fields

initial_price: f64

Initial stock price

mu: f64

Drift rate (excluding jump compensation)

sigma: f64

Continuous volatility

lambda: f64

Jump intensity (jumps per year)

jump_mean: f64

Mean of log jump size

jump_std: f64

Std of log jump size

Implementations

impl MertonJumpDiffusion

pub fn new(initial_price: f64, mu: f64, sigma: f64) -> Self

Create a new Merton Jump-Diffusion model

Default: no jumps (pure GBM)

pub fn with_jumps(self, lambda: f64, jump_mean: f64, jump_std: f64) -> Self

Configure jump parameters

Arguments

• lambda - Jump intensity (expected jumps per year)
• jump_mean - Mean of log jump size (negative for crashes)
• jump_std - Standard deviation of log jump size

pub fn expected_jump_contribution(&self) -> f64

Calculate expected jump contribution

Trait Implementations

impl Clone for MertonJumpDiffusion

fn clone(&self) -> MertonJumpDiffusion

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MertonJumpDiffusion

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

Formats the value using the given formatter.

impl SimulationModel for MertonJumpDiffusion

fn name(&self) -> &'static str

Get the model name

fn generate_path( &self, rng: &mut MonteCarloRng, time_horizon: &TimeHorizon, path_id: usize, ) -> SimulationPath

Generate a single simulation path

fn generate_antithetic_path( &self, rng: &mut MonteCarloRng, time_horizon: &TimeHorizon, path_id: usize, ) -> SimulationPath

Generate an antithetic path for variance reduction