Geometric Brownian Motion (GBM)

Dear all,

I wrote this code to simulate stock price scenarios by using Geometric Brownian Motion for each business day in one year.

S_0=55.8;                            % initial price
drift= (mu_oil-sigma_daily_oil^2/2);     % drift
npaths= 3000 ;                  % number of simulations
nsteps=252;                                      
dt=1/252;                   % time sequence (ti-ti+1)
epsilon=randn(nsteps,npaths);    
Weiner= [zeros(1,npaths); cumsum(epsilon).*sqrt(dt)] ;
S_t= bsxfun(@plus, drift*dt, sigma_daily_oil*Weiner);
S_t=S_0*exp(S_t) ; 

I would like to compute stock price scenarios only for grid points 1Y 2Y 3Y 4Y 5Y . Is correct to consider dt=1 and nsteps=5? Does anyone can help me , please?

Thank you

Martina

Answer 1

[Samatha Aleti]

Hi,

There is MATLAB class “gbm” to create Geometric Brownian Motion object. There are functions like simulate, simByEuler, simBySolution that can be used with gbm object for simulation. Here is the link for the documentation for further details:

https://www.mathworks.com/help/finance/gbm.html#d117e65554

https://www.mathworks.com/help/finance/sde.simulate.html

https://www.mathworks.com/help/finance/gbm.simbysolution.html

Also, you may set the parameters to get your desired behaviour as follows:

dt=1; 
nPeriods = 5; 
T = nPeriods * dt;