3 votes
Accepted

Characteristic function of a random variable by Fourier transform

I'll admit that I'm not familiar with most if not all stochastic finance terminology. So, I'll assume that $K$ and $S_{0}$ are constants. See that for $f(x)=\log(x)$, by Ito's Lemma, you get, \begin{...
Mr.Gandalf Sauron's user avatar
1 vote
Accepted

Find conditional probability that stock return will exceed some threshold value

Your computations are correct but the conclusions ar wrong.If two events cannot occur simultaneously they are not independent but mutually exclusive, i.e. they are the null event. That event has zero ...
finch's user avatar
  • 1,621
1 vote
Accepted

Regularity and B-S equation

As mentioned in https://en.wikipedia.org/wiki/Geometric_Brownian_motion we have $$S_{t}=S_{0}\exp \left(\left(\mu -{\frac {\sigma ^{2}}{2}}\right)t+\sigma W_{t}\right).$$ So the mapping $(\mu, \sigma)\...
Thomas Kojar's user avatar
  • 3,611
1 vote

derivate discounted payoff

I'd reason like this: first we can notice that in order for the argument to be different to zero, i must be that both $S < K$ and $S < \psi$. Hence we have two cases: $\psi > K$: in this ...
finch's user avatar
  • 1,621

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