Show that a security constitued by a Libor paid in advance has a model independantprice, that price being a linear combination of caplets (with differentstrikes) on the same libor.Thanks

Let X and Y be two gaussian random variables N(0, x) and N(0, y). X andY are correlated with a correlation .What is the law of E (X − Y |2X + Y )It seems very tedious to calculate the mean and variance of E(x-y|2x+y) directly from f(x,y).Any better ideas?Thanks

<t>quantyst. Perfect and detailed solution.Thanks so much. I should have the ability to handle this kind of probability problem, Please correct me.For random walk, use conditional distribution like the solution you give or Martingale form of y_n=t^x_nFor Brownian Motion, use Martingale form of Yt=ex...

<t> quantyst, Got you. Thanks for detailed solution.For the martingale, my main questions is how we get the equation 1/2(x^2 + 1/x) = 1?Under the condition that y_n is martingale.As my understanding, x_n can be approximated by x_t=0.5*t+1.5*W_t to match the mean and variance.when we set y_n=x^x_n. W...

<t>quantyst, Great solution.But with a(n)=x^n, you will get x^2+1/x=2. The solution of x is [sqrt(5)-1]/2Then a(n)={(sqrt[5]-1)/2}^(n) and a(0)=1It seems that your solution is the same as my solution 1. Can you give me some clue how the martingale give the same equation.I really don't get "The condi...

<t>start at 0 on a number line, flip a fair coin, move +2 on heads and -1 on tails,what is the probability that it will hit -1? (what if with biased coin, prob p for +1 and 1- for -1)I saw some post on other website, but I don't reconcile different solutions.Solution 1:x_n = x_{n-1} + z_nx_0 = 0, z_...

Thanks so much.I searched cylinders keyword. Nothing comes out.My bad.

Suppose that 2 cylinders each with radius 1 intersect at right angles and their centers also intersect. what is the volume of the intersections?Thanks

<t>What we want to minimize is the objective function f=Sum_(i=1 to m)(Fi^2)+Sum_(i=1 to n)(Pi^2). Please note that m is the number of functions, Fi , to be evaluated, and n is the number of variables, Pi is the penalty term.If we add each penalty term to each objective term, the objective function ...

<t>Cuchulainn, thanks for your suggestions. As you mentioned, then each penalty is added to EACH objective term. The main problem is here is that this penalty will mix up with the objective term as there is square in the later calculation(for the Aglib code or Lourakis, we can only provide each obje...

<t>When the penalty function term can be added directly to EACH objective term, the summation of which is the objective function. The problem can solved through Lourakis C++ Implementation of constrained LM.But what if the penalty terms are summed independently and then added to the objective functi...

<t>Hi, AllAs a lot of you may have implemented the model or be very good at interest rate models, it'd be greatly appreciated for your advice.I am trying to calibrate the CEV model to Caps according to the Hull and White's paper:Forward Rate Volatilities, Swap Rate Volatilities and the implementatio...