you don't need $ud=1.$ In fact, there are now about 30 binomial trees which converge to Black--Scholes in the large step limit. Most of them do not have $ud=1.$ All you need is $$ d < e^{r \Delta t}... Read More

In fact, OAS reflects none of the factors mentioned in the question. To begin with, the technical interpretation of OAS is that is it is the free money you earn for holding an MBS, for the following... Read More

What you seem to be missing is $$\sum{i,j} wi wj \sigmai \sigmaj = \left(\sumi wi\sigmai\right)^2$$ Now apply Jensen's inequality to get $$\left(\sumi wi\sigmai\right)^2 \leq \sumi wi\sigmai^2 $$ QED... Read More

I haven't encountered them, but if you mean " * _Hebel-Zertifikate_* " as defined on Wikipedia they just seem to be leveraged certificates with an obligatory stop-loss knock-out. Those turbo warrants... Read More

For any process with independent increments, by the very fact of statistical independence the variance of $x{t3}-x{t1}$ is going to be the sum of the variances of $x{t2}-x{t1}$ and $x{t3}-x{t2}$ for... Read More

I would use the following arguments: If the option were on the first throw of the dice, then we would price it using the expectation, which is $3.5$ (= $(1+2+\cdots+6)/6$. Now we have a 2 stage game:... Read More

honestly your question is hard to understand. Are these two questions the same? "Does fitting sub-optimal option exercise strategies to market data yield better option values?" "which modeling appro... Read More

Yes, it can work. However, keep in mind that: you'll be safer if you don't share any objects between threads; see my answer here, in particular the last point; even if you use different seeds, there... Read More

Except in highly unusual cases, financial PDEs lack analytic solutions. The mathematical tools used are Monte Carlo, plus the usual ones for solving PDEs on grids, almost always one of the following:... Read More

For a non-listed company you usually have a poor idea of the share value. If you do not know the underlying price it is impossible to accurately estimate the option price. So, for cases like this, pe... Read More