Fix n. Let p=prob of generating 1's and p_k = prob of generating k 1's out of n independent trials. Then p_k reaches its maximum at around p(n+1)-1.

For any positive interger N, letm(N,t) = E( (W_t)^N )The use Ito's formula, you can getdm(N,t) = N(N-1)/2 * m(N-2,t)dtWhen N=1, m(1,t) = 0. So for all odd N, m(N,t) = 0. For N=0, E(0,t) =1. So mathematical induction provids the result as you have stated for even N.

Is there any site similar to these two that covers interest rate related issues/products/papers and updates on a weekly basis?

Just saw this from the latest issue of "Mathematical Finance". May be helpful.THE BLACK-SCHOLES EQUATION REVISITED: ASYMPTOTIC EXPANSIONS AND SINGULAR PERTURBATIONSMartin Widdicks, Peter W. Duck, Ari D. Andricopoulos, David P. Newton

The paper from March 2005 issue of Risk,Replication of flexi-swapsby Ingmar Evers amd Farshid Jamshidian, might be helpful.Yeren

<t>How about this one?-----------JP Morgan Completes CDO CubedBankers at JP Morgan confirm that the bank has recently arranged what may well count as the market's first CDO-cubed - that is, a CDO of CDOs of CDOs. The private synthetic transaction, which closed several weeks ago, consisted of a simpl...

The difference is basical from the funding cost.

<t>The value of any tranche depends on how much protection it can provide. Intuitively, when the correlation increases, it takes fewer credit events to wipe out the equity tranche, and hence provides less protection from this tranche. You can find more rigorous proof of this claim from the paper by ...

There is a recent artical from derivativeweek (in learning curve section) from Alex Reyfman discussed this topic (about recovery hedge) for the CDO tranches on TRAX/CDX. That may be helpful.Yeren

Letest issue of "Derivative Week" has a paper called:Introducing Base CorrelationThis may be related to your topic.Yeren

I am looking for a copy of the following papers:W. Schmidt: Pricing irregular interest cashflowsD. Pugachevsky: CMS rates and adjustment for stochastic discountsIf you have a copy or know where to obtain them on the net, please let me know.Appreciate your help.Y.

<t>Could you please tell me how the deal get structured for CM DFS? The protection seller still pays 1-R if R is the recovery rate upon default. How about the buyer? I have seen many DFS deal that we called floaters where the premium pay 3M Libor + spread. Is this related to the this kind of CM DFS ...

Will http://www.bis.org/publ/bcbsca.htm help?

<t>Try Bjork's book first: Arbitrage theory in continuous timewhich I will regarded as the one of the best text books. If you like more math flavors, then the following two books are good references too:Interest Rate Models: Theory and Practiceby Damiano Brigo and Fabio MercurioMartingale Methods in...

<t>Or in a different way:Take two correlated BM B(t) and W(t) such thatdB(t) . dW(t) = rhoand conside the process:f(B, W) = exp( a*B(t) + b*W(t) )N apply the Ito's lemma and then take expectation on df(B, W), you will getE( exp(a*B(1) + b*W(1) )= exp[ (a^2 + 2 * rho * a * b + b^2 ) * t / 2 ]Please n...