sim — Price Process Simulation

Stochastic process simulation for commodity price modelling and Monte Carlo. Process selection is driven by the cluster type of the commodity being modelled.

Process selection by cluster:

Key Functions

ou(theta, mu, sigma, n, dt=1/252, x0=None, nSims=1): Ornstein-Uhlenbeck mean-reverting process. Primary model for Cluster A.
gbm(mu, sigma, nSteps, nSims, s0=100, dt=1/252): Geometric Brownian Motion. Standard for energy-linked clusters.
levyOu(theta, mu, sigma, jumpIntensity, jumpMean, jumpStd, n, dt=1/252): Lévy OU — OU process with superimposed compound Poisson jumps.
compoundPoisson(lam, jumpMean, jumpStd, n, dt=1/252, seed=None): Compound Poisson process for event-triggered demand (Cluster B: road salt; Cluster T: floral events).
markovSwitching(states, transitionMatrix, stateMeans, stateSigmas, n, seed=None): Hidden Markov regime-switching process. Use for markets with regulatory regimes (Cluster R) or weather state transitions (Cluster B).
garch(omega, alpha, beta, n, mu=0.0, seed=None): GARCH(1,1) conditional volatility. Calibrate with fit.fitGarch().
heston(S0, v0, kappa, theta, xi, rho, r, T, nSteps, nSims, seed=None): Heston stochastic volatility model. For markets with vol-of-vol dynamics.
arma(ar, ma, n, sigma=1.0, mu=0.0, seed=None): ARMA(p,q) process for serially correlated price drivers.
poisson(lam, n, seed=None): Homogeneous Poisson process for event counting.
simulate(model, params, n, nSims=1, seed=None): General dispatcher: pass model name as string and params dict.

import sipQuant as sq
import numpy as np

# Cluster A — OU process for Alberta Hay (calibrated from fit.fitOu)
paths = sq.sim.ou(
    theta=0.85,   # mean reversion speed (weekly)
    mu=187.50,    # long-run mean price
    sigma=8.20,   # volatility $/tonne per week
    n=52,         # 1 year of weekly steps
    dt=1/52,
    x0=185.0,
    nSims=1000,
)
# paths shape: (1000, 52)

# Cluster B — Compound Poisson for weather-event demand
jumps = sq.sim.compoundPoisson(
    lam=2.5,      # 2.5 demand events per year
    jumpMean=35.0, # avg price spike $/tonne
    jumpStd=12.0,
    n=52,
    dt=1/52,
    seed=42,
)

# Cluster R — Markov switching for regulatory regime
transition = np.array([[0.95, 0.05],   # stable → disrupted: 5%/period
                        [0.20, 0.80]])  # disrupted → stable: 20%/period
regime_paths = sq.sim.markovSwitching(
    states=2,
    transitionMatrix=transition,
    stateMeans=np.array([185.0, 320.0]),   # stable vs disrupted price
    stateSigmas=np.array([8.0, 45.0]),
    n=52,
    seed=42,
)