<t>maybe there is something I am missing here... If you look at the characteristic function of X^3 where X is normally distributed it doesn't seem to produce anything like exp(itmu - t^2sigma^2).... and if it was still normal, its kurtosis would be three and its skewness would be zero like all norma...

Hi,If v has a two parameter weibull distribution, how is v^3 distributed?and if v is normal , how is v^3 distributed?(the weibull one I can sort of work out, but am not sure my answer is right...)Any help will be much appreciated.Cheers

<t>Ok, so under the risk neutral measuredS_t = r S_t dt + sigma S_t dWt (if you are doing this in the normal BS framework)Solving this SDE gives usS_t= S_0exp((r-0.5sigma^2)t + sigmaW_t)so So Ln(S_t/X) is normally distributed with mean = ln(S_0/X) +(r-0.5*sigma^2)t and variance sigma^2 tThe value V ...

<t>What is S? what is X?But generally yes... if you can find the dynamics of S/X under the risk neutral measure then you can price the security. Depending on the dynamics it may have to be done numerically, but I would say that in this case a closed fom is likely.If for instance S/X is lognormal, (s...

<t>Hi all,I am trying to model output of an aggregation of wind farms. The output is a function of the wind speed (v) and the yield curve for the turbine in question say P(v) and v is distributed according to a weibull distribution with parameters dependent on the specific site. How would you model ...

There is quite a lot in the literature about summing lognormals esp. with a view to pricing baskets. You can get quite tight bounds using comonotonicity and conditioning, but no closed forms.

Also have a look at Schwartz' 2 factor model. It gives closed form solutions for commodity forwards, so you can calibrate the model to fit your historic data using MLE or similar, and then use the formula to get your forward prices.

<t>Hi,What is probability you have ?? the probability that asset i defaults in period t given that it hasn't defaulted in beforeIf this is the case you can sample 30 correlated uniform random variables to obtain a sample default set for your assets. (since F^{-1}_X(U) ~ X)This can then be pugged int...

Hi,Why don't you use a first passage model (where company defaults as soon as its asset value falls below a certain level)...I know asset vaue and stock price are not the same thing but it might be worth looking into...(Do you want the deault time or the probability of deafult?)

What is X... what is Y?how are they distributed?

Actually I thought it used the Kreps -Yan separation theorem.In Schachermayer (2003).This is why I started reading up on FA in the first place...trying to understand that paper.

Firstly, if you are considering a European option don't create the whole path. Just generate a sample from the terminal distribution.From there it is easy to add in various standard variance reduction techniques.

<t>Usually in securitisation models you simulate the cash flows from your assets and deduct losses from this amount. The losses occur with some probability distribution, so you can do a monte carlo simulation to find out when the loss occurs and how bad it is.This will give you your expected cash fl...

<t>Hi,Both of these methods model the number of defaults in a pool. So if you have one asset, you couldn't use them.BET just uses the binomial distribution to give you a probability of the X defaults in a pool, and the gaussian copula approach is to model correlated lognormal variables by simulating...

<t>QuoteWhere do people need the ideas, theorems and results of Functional Analysis in their daily work in Financial Engineering? Of course, it's great knowing FA but is is directly relevant? I am not talking about measure theory, Fourier analysis and so on but am referring to subjects like:I'm read...