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x~N(0,1)How to solve the expectation of exp(exp(x))? Thanks!

It explodes.

The moment generating function of the lognormal distribution is only defined on the negative real axis, but not on the positive half-line.One way to see it is: take the characteristic function of the lognormal, expand it by Taylor series. And then you see that this series diverge on the positive half-line.Did you actually try in the first place?The point of the forums is to show that you tried something, it gives more incentive to people to help you.Best,

Does anyone has an idea why this converges for trees methods,for example when using log-normal short rates models (BDT or Dothan) the cash expectation Eexp(int _0^t r_s ds) converge where even the expectation is not defined. Eexp(exp(N)) ??

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I came accross this problem. First to see the divergence just write which shows that the chi-2 diverges as well. In practise you need to discretize your model and assume not continuous compounding. A funny thing is that when scaled by the volatiltily the divergence can happens quite far and some numerical integration schemes can miss out.

QuoteOriginally posted by: quantiquequantDoes anyone has an idea why this converges for trees methods,for example when using log-normal short rates models (BDT or Dothan) the cash expectation Eexp(int _0^t r_s ds) converge where even the expectation is not defined. Eexp(exp(N)) ??i don't think it does converge in the Dothan model.BDT get round the problem by using a binomial tree. So whilst the limit process has the issue, the approximating tree does not.