Các câu hỏi phỏng vấn [18/8/2007]

[YADD]

Originally Posted by nguyenxuanson

quay lai bai cua anh YADD, hoa ra de cua bac la tren hinh cube huu han a, cu tuong mang regular vo han giong nhu trong polymer

cau nay chac nhieu nguoi biet roi:

Well, it was supposed to be a 5-10 minute interview question, wasn't it? What I liked about the question is its elegant solution. It goes as follows: Let's record a pattern of the random walker on the cube; every site must be visited as frequently as others. Therefore the average distance of two successive visits to the same site is 8.

N door, behind one door there is a GOLD BAR, other N-1 do not have GOLD BAR. You select one door.

Then I open another door and I do not have the GOLD BAR. Would you, in this situation, exchange your door with one of N-2 door left?

This question is standard. I should.

Say, N=100. The probability that the gold bar lies behind the door I picked is 1%. That is, the probability that the gold bar lies behind the other 99 doors is 99%. Now, with one door opened, the probability that each one of the other 98 remaining doors to have the gold bar is 99% divided by 98 which is greater than 1%.

[YADD]

Originally Posted by shinichi9htv

Carr formula shows us how to replicate every contingent claim statitically by a set of fwd, out the money calls and puts:

(smt like that, perhaps you could find an exact formula with "static hedging")

I think the cliquets give us a "forward smile" - a prediction of smile.

(Missed this one...)

This formula is well popularized. But it is for European-type options only. No path dependency, no early exercise.

Originally Posted by drew

Well, every european contingent claim (convex payoff, whatever...) can be replicated by a bunch of calls (or puts), now if you throw in the cliquets (a call is nothing but a cliquet with T_1 = 0), you can cover all path-dependent options.
Regarding the hedge, does vol need to be deterministic ? I think this semi-static hedge always works no matter what the vol is.

So what is the master formula (a la Carr above) or algorithm?

Please. Just give me the elusive result. End of story.

[spin]

Originally Posted by spin

19) Consider three i.i.d random variables on [0,1] U_{1}, U_{2} and U_{3}. Calculate E[min(U_{1},U_{2},U_{3})]

Another one :

Let's U$_{(1)}$ =min(U$_{1}$,U$_{2}$) and U$_{(2)}$ =max(U$_{1}$,U$_{2}$). Calculate
E[max(U$_{(1)}$,U$_{(2)}$-U$_{(1)}$,1-U$_{(2)}$)]

[nguyenxuanson]

x=U$_{(1)}$
y=U$_{(2)}$-U$_{(1)}$
z=1-U$_{(2)}$=1-x-y
all have distribution P(x\in[k,k+dk])=2(1-k)dk with k\in[0,1]
all independent(not quite sure)
if it is the case then use the previous question.

[Hung.Q.Ngo]

20. Does the sequence go to infinity as tends to infinity? (Note: it's a sequence, is an integer.)

21. Is the above sequence dense in ?

[spin]

Originally Posted by nguyenxuanson

x=U$_{(1)}$
y=U$_{(2)}$-U$_{(1)}$
z=1-U$_{(2)}$=1-x-y
all have distribution P(x\in[k,k+dk])=2(1-k)dk with k\in[0,1]
all independent(not quite sure)
if it is the case then use the previous question.

seems incorrect!!

So, the result is....??

[nguyenxuanson]

20/ no, for all N>0 and epsilon >0 we can find n>N such that n|sin(n)|<epsilon.

[nguyenxuanson]

no short cut, brute force:

insert

the first term

....

[drew]

20) Using theorem 1.3 in here for alpha = 1 / PI,
|1 / PI - a / q | < 1 / q^2 for infinitely many integers q
==> |q - a * PI| < PI / q
==> |sin q| < PI / q if q is large enough
==> q |sin q| < PI if q is large enough

[drew]

21) Well, yeah ! So, how ? Well, let me dig sth up later :-) !