sim module

btQuant.sim.ar1(phi, intercept, sigma, nSteps, nSims, x0=0.0)

AR(1) process simulation.

Parameters:

• phi – autoregressive coefficient

• intercept – constant term

• sigma – error variance

• nSteps – number of time steps

• nSims – number of simulations

• x0 – initial value

Returns:

array (nSims x nSteps)

btQuant.sim.arch(alpha0, alpha1, nSteps, nSims)

ARCH(1) process simulation.

Parameters:

• alpha0 – constant term

• alpha1 – ARCH coefficient

• nSteps – number of time steps

• nSims – number of simulations

Returns:

array (nSims x nSteps)

btQuant.sim.arma(arCoefs, maCoefs, sigma, nSteps, nSims, x0=0.0)

ARMA process simulation.

Parameters:

• arCoefs – AR coefficients (list)

• maCoefs – MA coefficients (list)

• sigma – error std deviation

• nSteps – number of time steps

• nSims – number of simulations

• x0 – initial value

Returns:

array (nSims x nSteps)

btQuant.sim.cir(kappa, theta, sigma, nSteps, nSims, r0=0.05, dt=0.003968253968253968)

Cox-Ingersoll-Ross (CIR) interest rate model simulation.

Parameters:

• kappa – mean reversion rate

• theta – long-term mean

• sigma – volatility

• nSteps – number of time steps

• nSims – number of simulations

• r0 – initial rate

• dt – time step

Returns:

array (nSims x nSteps)

btQuant.sim.compoundPoisson(lambdaRate, jumpMu, jumpSigma, nSteps, nSims, s0=100, dt=0.003968253968253968)

Compound Poisson process simulation (jumps with sizes).

Parameters:

• lambdaRate – jump intensity

• jumpMu – mean jump size

• jumpSigma – jump size std dev

• nSteps – number of time steps

• nSims – number of simulations

• s0 – initial value

• dt – time step

Returns:

array (nSims x nSteps)

btQuant.sim.garch(omega, alpha1, beta1, nSteps, nSims)

GARCH(1,1) process simulation.

Parameters:

• omega – constant term

• alpha1 – ARCH coefficient

• beta1 – GARCH coefficient

• nSteps – number of time steps

• nSims – number of simulations

Returns:

array (nSims x nSteps)

btQuant.sim.gbm(mu, sigma, nSteps, nSims, s0=1.0, dt=0.003968253968253968)

Geometric Brownian Motion simulation.

Parameters:

• mu – drift

• sigma – volatility

• nSteps – number of time steps

• nSims – number of simulations

• s0 – initial value

• dt – time step

Returns:

array (nSims x nSteps)

btQuant.sim.heston(mu, kappa, theta, sigma, rho, s0=100, v0=0.04, nSteps=252, nSims=1000, dt=0.003968253968253968)

Heston stochastic volatility model simulation.

Parameters:

• mu – drift of stock price

• kappa – mean reversion rate of variance

• theta – long-term variance

• sigma – volatility of variance

• rho – correlation between stock and variance

• s0 – initial stock price

• v0 – initial variance

• nSteps – number of time steps

• nSims – number of simulations

• dt – time step

Returns:

dict with ‘prices’ and ‘variances’ arrays (nSims x nSteps)

btQuant.sim.levyOu(theta, mu, sigma, jumpLambda, jumpMu, jumpSigma, nSteps, nSims, x0=0.0, dt=0.003968253968253968)

Lévy OU process (OU with jumps) simulation.

Parameters:

• theta – mean reversion rate

• mu – long-term mean

• sigma – diffusion volatility

• jumpLambda – jump intensity

• jumpMu – jump mean

• jumpSigma – jump volatility

• nSteps – number of time steps

• nSims – number of simulations

• x0 – initial value

• dt – time step

Returns:

array (nSims x nSteps)

btQuant.sim.markovSwitching(mu1, sigma1, mu2, sigma2, p11, p22, nSteps, nSims, x0=0.0)

Markov regime switching model simulation.

Parameters:

• mu1 – mean in regime 1

• sigma1 – std dev in regime 1

• mu2 – mean in regime 2

• sigma2 – std dev in regime 2

• p11 – probability of staying in regime 1

• p22 – probability of staying in regime 2

• nSteps – number of time steps

• nSims – number of simulations

• x0 – initial value

Returns:

array (nSims x nSteps)

btQuant.sim.ou(theta, mu, sigma, nSteps, nSims, x0=0.0, dt=0.003968253968253968)

Ornstein-Uhlenbeck process simulation.

Parameters:

• theta – mean reversion rate

• mu – long-term mean

• sigma – volatility

• nSteps – number of time steps

• nSims – number of simulations

• x0 – initial value

• dt – time step

Returns:

array (nSims x nSteps)

btQuant.sim.poisson(lambdaRate, nSteps, nSims)

Poisson process simulation (jump counts).

Parameters:

• lambdaRate – jump intensity (jumps per period)

• nSteps – number of time steps

• nSims – number of simulations

Returns:

array (nSims x nSteps)

btQuant.sim.simulate(model, params, nSteps, nSims)

General simulation dispatcher.

Parameters:

• model – model name (str)

• params – dict of model parameters

• nSteps – number of time steps

• nSims – number of simulations

Returns:

array of simulated paths

btQuant.sim.vasicek(kappa, theta, sigma, nSteps, nSims, r0=0.05, dt=0.003968253968253968)

Vasicek interest rate model simulation.

Parameters:

• kappa – mean reversion rate

• theta – long-term mean

• sigma – volatility

• nSteps – number of time steps

• nSims – number of simulations

• r0 – initial rate

• dt – time step

Returns:

array (nSims x nSteps)