gbm_simulator module

gbm_simulator.dispatch_simulation(n, s, r, div_yield, dt, sigma, z, method)

Dispatch the simulation to the appropriate algorithm

gbm_simulator.simulate_gbm(n, s, r, div_yield, t, t_terminal, dt, sigma, method='euler', seed=None)

Simulate a geometric brownian motion path

The GBM is simulated using either the Euler or Milstein method. Instead of a loop, the algorithms have been vectorized for speed.

Euler:

\(S_{t+1} = S_{t} + \mu S_{t} dt + \sigma S_{t} \sqrt{dt} Z_{t+1}\)

Milstein:

\(S_{t+1} = S_{t} + \mu S_{t} dt + \sigma S_{t} \sqrt{dt} Z_{t+1} + .5 \sigma ^ 2 ((\sqrt{dt} Z_{t+1}) ^ 2 - dt)\)

Parameters:

• n (double) – The number of paths to simulate
• s (double) – Initial stock price at time t.
• r (double) – The risk free interest rate.
• div_yield (double) – Dividend yield.
• t_terminal (double) – Terminal time T
• t (double) – Starting time
• dt (double) – Discretization time step size
• sigma (double) – Volatility
• method ({"euler", "milstein"}, defaults "euler") – Numerical method to simulate with
• seed (int) – Random seed to set for random normal generation

Returns:

sims – An array containing the n simulations as rows and the time steps as columns

Return type:

Numpy array

See also

option_value.price_option()

gbm_simulator.simulate_gbm_euler(n, s, r, div_yield, dt, sigma, z)

GBM simulation using a Euler discretization

gbm_simulator.simulate_gbm_milstein(n, s, r, div_yield, dt, sigma, z)

GBM simulation using a Milstein discretization