S_t and dS_t

[jensen]

what is the relation between these?

1) St = So . exp (r-sigmaˆ2/2)t + sigma . Zt

2) dSt = St . [mu.dt + sigma.dZt]

 

[examstudent]

solve the SDE by calculating dLnSt from dSt (ITO lemma), then integrate out, then exponentiate.

 

[jensen]

solve the SDE by calculating dLnSt from dSt (ITO lemma), then integrate out, then exponentiate.

you meant (2) becomes (1)? so i have :

dlnSt = mu.dt + sigma.dZt ---(3)

then I let f = (3)

using ito lemma

df = df/dt.dt +df/dS.dS + 1/2 d2f/dS2.dt

how do i substitute in?

thanks examstudent.

 

[examstudent]

cant undertsand your notation, but my notation is crap,

but f= ln S
and df/ds =1/s
and 2nd deriv = -1/S^2

 

[jensen]

cant undertsand your notation, but my notation is crap,

but f= ln S
and df/ds =1/s
and 2nd deriv = -1/S^2

oh i see it now. df/dt = 0 and that the resulting r is actually mu.

Cheers examstudent!