I have a very specific question. For a one factor Hull-White short-term interest rate trinomial tree, we can replacer(j, k) = r(0, k) * exp (j * q)k: stepq: vol * sqrt ( 3 * delta(T) )r(0, k): forward rate from k to k+1with another oner(j, k) = r(0, k) * [ ( Exp( w * j * q) - 1 ) /w + 1];so when w = 1, it is log normal distribution, the same as the old equation.when w-->0, it is a normal distrubtion. r(j, k) = r(0, k) * ( 1 + j * q);And we know that when we are calibrating the discount factor, we want to keep the vol unchanged, while changing the mean. This meansvar[ f(r) ] = unchanged.In the case of lognormal-distribution, f(r) = log(r), and in the case of normal-distribution, f(r) = r. So when you have lognormal distribution, you adjust k step's interest rate by a * r. And when you have normal distribution, you should adjust it by a + r.Now the question is that if anything between normal and lognormal ( 0 < w < 1), what f(r) should you choose, and how should you adjust?