Struct KouJumpDiffusionProcess 

pub struct KouJumpDiffusionProcess { /* private fields */ }

Model describes stock price with continuous movement that have rare large jumps, with the jump sizes following a double exponential distribution.

LaTeX Formula

• dS_{t} = \mudt + \sigmadW_{t} + d(sum_{i=1}^{N(t)}(V_{i}-1))\n where V_{i} is i.i.d. non-negative random variables such that Y = log(V) is the assymetric double exponential distribution with density:\n
• f_{Y}(y) = p*\eta_{1}e^{-\eta_{1}y}\mathbb{1}_{0\leq y} + (1-p)\eta_{2}*e^{\eta_{2}y}\mathbb{1}_{y<0}

Links

• Wikipedia: N/A
• Original Source: https://dx.doi.org/10.2139/ssrn.242367

Examples

use ndarray::Array1;
use digifi::utilities::TEST_ACCURACY;
use digifi::stochastic_processes::{StochasticProcessResult, StochasticProcess, KouJumpDiffusionProcess};

let n_paths: usize = 1_000;
let n_steps: usize = 200;

let kjd: KouJumpDiffusionProcess = KouJumpDiffusionProcess::build(0.2, 0.3, 0.5, 9.0, 5.0, 0.5, n_paths, n_steps, 1.0, 100.0).unwrap();
let sp_result: StochasticProcessResult = kjd.simulate().unwrap();

assert_eq!(sp_result.paths.len(), n_paths);
assert_eq!(sp_result.paths[0].len(), n_steps + 1);
assert_eq!(sp_result.expectations_path.clone().unwrap().len(), n_steps + 1);
assert_eq!(sp_result.variances_path.unwrap().len(), n_steps + 1);
assert!((sp_result.mean - sp_result.expectations_path.unwrap()[n_steps]).abs() < 20_000_000.0 * TEST_ACCURACY);

Implementations

impl KouJumpDiffusionProcess

pub fn build( mu: f64, sigma: f64, lambda_n: f64, eta_1: f64, eta_2: f64, p: f64, n_paths: usize, n_steps: usize, t_f: f64, s_0: f64, ) -> Result<Self, DigiFiError>

Creates a new KouJumpDiffusionProcess instance.

Input

• mu: Mean of base stochastic process (i.e., process without jumps)
• sigma: Standard deviation of base process (i.e., process without jumps)
• lambda_n: Rate of jumps
• eta_1: Rate parameter of the positive jumps
• eta_2: Rate parameter of the negative jumps
• p: Probability of a jump up
• n_paths: Number of paths to generate
• n_steps: Number of steps
• t_f: Final time step
• s_0: Initial value of the stochastic process

Errors

• Returns an error if the argument p is not in the range [0,1].

Trait Implementations

impl Debug for KouJumpDiffusionProcess

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

Formats the value using the given formatter.

impl ErrorTitle for KouJumpDiffusionProcess

fn error_title() -> String

Returns the error title.

impl StochasticProcess for KouJumpDiffusionProcess

fn get_expectations(&self) -> Option<Array1<f64>>

Calculates the expected path of the Kou Jump-Diffusion process

Output

• An array of expected values of the stock price at each time step

LaTeX Formula

• E[S_t] = S_{0} + t(\mu + \lambda_{n}(\frac{p}{\eta_{1}} - \frac{1-p}{\eta_{2}}))

fn get_variances(&self) -> Option<Array1<f64>>

Calculates the variance of the Kou Jump-Diffusion process.

Output

• An array of variances of the process at each time step

LaTeX Formula

• Var[S_{t}] = t(\sigma^{2} + 2\lambda_{n}(\frac{p}{\eta^{2}{1}} + \frac{1-p}{\eta^{2}{2}}))

fn get_paths(&self) -> Result<Vec<Array1<f64>>, DigiFiError>

Generates simulation paths for the Kou Jump-Diffusion process.

Output

• Array of simulated paths following the Kou Jump-Diffusion process

LaTeX Formula

• dS_{t} = \mudt + \sigmadW_{t} + d(sum_{i=1}^{N(t)}(V_{i}-1))\n where V_{i} is i.i.d. non-negative random variables such that Y = log(V) is the assymetric double exponential distribution with density:\n
• f_{Y}(y) = p*\eta_{1}e^{-\eta_{1}y}\mathbb{1}_{0\leq y} + (1-p)\eta_{2}*e^{\eta_{2}y}\mathbb{1}_{y<0}

fn update_n_paths(&mut self, n_paths: usize)

Updates the number of paths that the stochastic process will generate.

fn get_n_steps(&self) -> usize

Returns the number of time steps in the stochastic process.

fn get_t_f(&self) -> f64

Returns the final time step.

fn simulate(&self) -> Result<StochasticProcessResult, DigiFiError>

Runs stochastic process simulation: