When one applies Ito lemma for logarithmical transformation of price process that follows GBM, one obtains
St = So*exp( (mu - sigma^2/2)dt + sigma * dWt).
If one further applies Monte Carlo simulation dt is replaced by detla t (i.e. one goes from infinitesimal time steps to larger time steps, eg. 5 out of 250 days as in the example) and dWt is replaced by epsilon* SQRT(delta t).
In the solutions the above formula was not taken into account, but GBM dynamics was directly decomposed to
(St - So) / So = mu*delta t + sigma * epsilon * SQRT (delta t), that is:
St = So + So * (mu*delta t + sigma * epsilon * SQRT (delta t))
Why?
Thanks.
St = So*exp( (mu - sigma^2/2)dt + sigma * dWt).
If one further applies Monte Carlo simulation dt is replaced by detla t (i.e. one goes from infinitesimal time steps to larger time steps, eg. 5 out of 250 days as in the example) and dWt is replaced by epsilon* SQRT(delta t).
In the solutions the above formula was not taken into account, but GBM dynamics was directly decomposed to
(St - So) / So = mu*delta t + sigma * epsilon * SQRT (delta t), that is:
St = So + So * (mu*delta t + sigma * epsilon * SQRT (delta t))
Why?
Thanks.
