J**********g
发帖数: 213 | 1 Just done the interview with FID at MS. Messed it up. I thought he would ask
about the techinical problems, and it turned out that brainteaser and
statistics problem. I guess he had database to pick up problems from.
first question.
1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
a call option with strike price of 100.
Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
2. choose three points on a circle and form a triangle. ask the probability
of triangle is a right triangle.
No clue. I know I can google it at the time. I forgot it when I was doing it.
3. X and Y has a joint normal distribution. variances of X an Y are both 1,
and covariance is 1/sqrt(2). Ask the conditional probility of {x>0 |y<0}.
I seemed to be told the means of x and y to be zeroes, and I think they should be there too.
I knew I can apply something here, but I forgot it totally.
I prepared, based on my background, numerical analysis, stochastic calculus,
asset pricing, monte carlo simulation, C++, but not brainteaser and
statistics at all. So the lession is, brainteaser (probability) and
statistics are the things they care.
The ED is a PhD in physics, though he has developer experience, I should
have known what kinds of questions he would ask. Prepare ACCORDINGLY!
One more interview on Friday. This time from Commodities markets modeling,
and by Ehud Ronn, the leading modeler at MS.
http://www.linkedin.com/ppl/webprofile?vmi=&id=11441997&pvs=pp&authToken=RwUb&authType=name&locale=en_US&trk=ppro_viewmore&lnk=vw_pprofile
So what's your opinion of questions he might ask? I guess he might ask less
technical questions or brainteaser, but more like my opinion on certain
things.Here is one lecture he gave in May : Current perspectives on energy
derivatives, structured products and risk management
Really don't wanna blow it up again. thanks... |
J**********g
发帖数: 213 | 2 no time to blame myself, gotta prepare more now...
any suggestion about commodities markets? |
x**y
发帖数: 10012 | 3 这东西 说实话 能问的面太广泛..
【在 J**********g 的大作中提到】
: no time to blame myself, gotta prepare more now...
: any suggestion about commodities markets?
|
d*j
发帖数: 13780 | 4 check history in this board
check swordsman or bullettooth 's summary
try to answer all of those questions listed |
J**********g
发帖数: 213 | 5 Thank you. Just got time to google Ehud Ronn again..he is a big guy, and I
he is in his 50s and I wonder would he ask questions same as the the ED in
FID.
I really wish MS were not the first company that i interviewed in job career
...I would much better I had some interview experience before and I should
have got it...whatever...
【在 d*j 的大作中提到】
: check history in this board
: check swordsman or bullettooth 's summary
: try to answer all of those questions listed
|
b******e
发帖数: 118 | 6 第3题没有给X和Y的mean吗？
ask
price
probability
【在 J**********g 的大作中提到】
: Just done the interview with FID at MS. Messed it up. I thought he would ask
: about the techinical problems, and it turned out that brainteaser and
: statistics problem. I guess he had database to pick up problems from.
: first question.
: 1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
: would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
: a call option with strike price of 100.
: Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
: 2. choose three points on a circle and form a triangle. ask the probability
: of triangle is a right triangle.
|
c*******a
发帖数: 45 | |
c******r
发帖数: 300 | 8 No worry, practice makes perfect.
For 3, assume the means to be zero, let U,V,W be i.i.d. N(0,1)
then we can let
X = 1/sqrt{2}U-1/sqrt{2}V
Y = 1/sqrt{2}U-1/sqrt{2}W
p(X>0|Y<0)=p(X>0,Y<0)/P(Y<0)=P(U>V,U
ask
price
probability
【在 J**********g 的大作中提到】
: Just done the interview with FID at MS. Messed it up. I thought he would ask
: about the techinical problems, and it turned out that brainteaser and
: statistics problem. I guess he had database to pick up problems from.
: first question.
: 1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
: would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
: a call option with strike price of 100.
: Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
: 2. choose three points on a circle and form a triangle. ask the probability
: of triangle is a right triangle.
|
s*******u
发帖数: 35 | 9 好像不对吧。我的结果是0.25
第二题是0
【在 c******r 的大作中提到】
: No worry, practice makes perfect.
: For 3, assume the means to be zero, let U,V,W be i.i.d. N(0,1)
: then we can let
: X = 1/sqrt{2}U-1/sqrt{2}V
: Y = 1/sqrt{2}U-1/sqrt{2}W
: p(X>0|Y<0)=p(X>0,Y<0)/P(Y<0)=P(U>V,U:
: ask
: price
: probability
|
V******t
发帖数: 35 | 10 Do you mind sharing how the first problem was solved? |
|
|
l******f
发帖数: 568 | 11 你是硬积的还是有什么trick？周的书上130页有道题很像， symmetry用得很漂亮
楼上的solution也很漂亮， 不过没有justify X 和 Y是 joint normal
第二题是0.
【在 s*******u 的大作中提到】
: 好像不对吧。我的结果是0.25
: 第二题是0
|
c******r
发帖数: 300 | 12 En, I was treating the covariance to be 1/2 instead of 1/sqrt(2), but the
idea applies similarly, let
X = 1/\sqrt{2}(U-V)
Y = U
P(X>0|Y<0)=P(U>V,U<0)/P(U<0)= (1/8)/(1/2)=1/4
I think in general for rho > 0, the result will be
\frac{1}{pi}arctan(rho/\sqrt(1-rho^2))
【在 s*******u 的大作中提到】
: 好像不对吧。我的结果是0.25
: 第二题是0
|
n***e
发帖数: 13 | 13 2. 我的intuition也是0
P(组成直角三角形)=choose(3,2)*P(两点组成直径)
and P(两点组成直径)=P(fix第一个点，第二个点在直径另一端)=0 因为是continuous |
f*******y
发帖数: 988 | 14 joint normal不是写在题目里面么
【在 l******f 的大作中提到】
: 你是硬积的还是有什么trick？周的书上130页有道题很像， symmetry用得很漂亮
: 楼上的solution也很漂亮， 不过没有justify X 和 Y是 joint normal
: 第二题是0.
|
z****i
发帖数: 406 | 15 第2题是0。
形成锐角三角形的概率是1／4，对吧？
ask
price
probability
【在 J**********g 的大作中提到】
: Just done the interview with FID at MS. Messed it up. I thought he would ask
: about the techinical problems, and it turned out that brainteaser and
: statistics problem. I guess he had database to pick up problems from.
: first question.
: 1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
: would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
: a call option with strike price of 100.
: Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
: 2. choose three points on a circle and form a triangle. ask the probability
: of triangle is a right triangle.
|
f*******y
发帖数: 988 | 16 楼主，不是我说，这些题目都fail说明你准备实在不足
ask
price
probability
【在 J**********g 的大作中提到】
: Just done the interview with FID at MS. Messed it up. I thought he would ask
: about the techinical problems, and it turned out that brainteaser and
: statistics problem. I guess he had database to pick up problems from.
: first question.
: 1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
: would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
: a call option with strike price of 100.
: Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
: 2. choose three points on a circle and form a triangle. ask the probability
: of triangle is a right triangle.
|
d**********9
发帖数: 5215 | 17 zkss?
【在 z****i 的大作中提到】
: 第2题是0。
: 形成锐角三角形的概率是1／4，对吧？
:
: ask
: price
: probability
|
s*****r
发帖数: 2347 | 18 俺算了下，confirm 1/4
【在 z****i 的大作中提到】
: 第2题是0。
: 形成锐角三角形的概率是1／4，对吧？
:
: ask
: price
: probability
|
s*****r
发帖数: 2347 | 19 画个图，先固定2个点，求第三个点出现的概率
然后对第二个点积分
【在 d**********9 的大作中提到】
: zkss?
|
b******e
发帖数: 118 | 20 X = rho * U + sqrt(1-rho^2)*V, right?
For this problem,X = 1/sqrt(2)*(U+V), not (U-V)??
But the final answer is same, 0.25.
【在 c******r 的大作中提到】
: En, I was treating the covariance to be 1/2 instead of 1/sqrt(2), but the
: idea applies similarly, let
: X = 1/\sqrt{2}(U-V)
: Y = U
: P(X>0|Y<0)=P(U>V,U<0)/P(U<0)= (1/8)/(1/2)=1/4
: I think in general for rho > 0, the result will be
: \frac{1}{pi}arctan(rho/\sqrt(1-rho^2))
|
|
|
x******a
发帖数: 6336 | 21 -V and V makes no difference
【在 b******e 的大作中提到】
: X = rho * U + sqrt(1-rho^2)*V, right?
: For this problem,X = 1/sqrt(2)*(U+V), not (U-V)??
: But the final answer is same, 0.25.
|
b******e
发帖数: 118 | 22 怎么得到的啊？
【在 s*****r 的大作中提到】
: 俺算了下，confirm 1/4
|
z****i
发帖数: 406 | 23 3个点在同一个半圆的概率是3／4
【在 d**********9 的大作中提到】
: zkss?
|
x******a
发帖数: 6336 | |
b******e
发帖数: 118 | 25 嗯，这个方法好：）
【在 z****i 的大作中提到】
: 3个点在同一个半圆的概率是3／4
|
d**********9
发帖数: 5215 | 26 oh, good idea, thanks
【在 z****i 的大作中提到】
: 3个点在同一个半圆的概率是3／4
|
b******e
发帖数: 118 | 27 P(X>0|Y<0) = P(X>0,Y<0)/P(Y<0)
= P(U+V>0, U<0)/P(U<0)
= P(U<0,V>0,V>|U|)/P(U<0) -->这一步类似于周书上的做法（但我在
一次面试中被质疑。。。）
= (1/2*1/2*1/2)/(1/2) = 0.25
Is it correct?
【在 x******a 的大作中提到】
: -V and V makes no difference
|
s*****r
发帖数: 2347 | 28 画个图啊，一回事
【在 b******e 的大作中提到】
: P(X>0|Y<0) = P(X>0,Y<0)/P(Y<0)
: = P(U+V>0, U<0)/P(U<0)
: = P(U<0,V>0,V>|U|)/P(U<0) -->这一步类似于周书上的做法（但我在
: 一次面试中被质疑。。。）
: = (1/2*1/2*1/2)/(1/2) = 0.25
: Is it correct?
|
x******a
发帖数: 6336 | 29 那三个1/2的乘积怎么出来的?
我是这样想的
P(U+V>0, U<0)= P(-V
【在 b******e 的大作中提到】
: P(X>0|Y<0) = P(X>0,Y<0)/P(Y<0)
: = P(U+V>0, U<0)/P(U<0)
: = P(U<0,V>0,V>|U|)/P(U<0) -->这一步类似于周书上的做法（但我在
: 一次面试中被质疑。。。）
: = (1/2*1/2*1/2)/(1/2) = 0.25
: Is it correct?
|
o*p
发帖数: 77 | 30 problem 3
1/4 ?
suppose x,y are N(0,1)
then Cholesky decomposition x=rho*y+sqrt(1-rho^2)*z
y, z are independent
rho is correlation between x and y =1/sqrt(2)
draw graph in y ,z plane
then p(x>0|y<0)
=p(x>0 intersect with y<0）/p(y<0)=(1/8)/(1/2)=1/4 |
|
|
b******e
发帖数: 118 | 31 Yes. You are right. Drawing graph is more clear.
【在 o*p 的大作中提到】
: problem 3
: 1/4 ?
: suppose x,y are N(0,1)
: then Cholesky decomposition x=rho*y+sqrt(1-rho^2)*z
: y, z are independent
: rho is correlation between x and y =1/sqrt(2)
: draw graph in y ,z plane
: then p(x>0|y<0)
: =p(x>0 intersect with y<0）/p(y<0)=(1/8)/(1/2)=1/4
|
y*******o
发帖数: 6632 | 32 Can we use the following to solve the problem? I am a newbie of
probabilities.
Cov(X,Y)=E(XY)-E(X)*E(Y)
SO
1/2=E(X<0,Y>0)-E(X<0)*E(Y>0)
1/2=E(X<0,Y>0)-1/2 * 1/2
SO
E(X<0,Y>0)=1/4
【在 c******r 的大作中提到】
: No worry, practice makes perfect.
: For 3, assume the means to be zero, let U,V,W be i.i.d. N(0,1)
: then we can let
: X = 1/sqrt{2}U-1/sqrt{2}V
: Y = 1/sqrt{2}U-1/sqrt{2}W
: p(X>0|Y<0)=p(X>0,Y<0)/P(Y<0)=P(U>V,U:
: ask
: price
: probability
|
t*******y
发帖数: 637 | 33 第一题怎么replicate?
ask
price
probability
【在 J**********g 的大作中提到】
: Just done the interview with FID at MS. Messed it up. I thought he would ask
: about the techinical problems, and it turned out that brainteaser and
: statistics problem. I guess he had database to pick up problems from.
: first question.
: 1. a stock has a price of 100 and a bond is 85. Tomorrow the stock price
: would be 110 or 90, and bond price would be 85 and 90 correspondingly. price
: a call option with strike price of 100.
: Using replicating portfolio. Answer is 6. Attention: no risk-neutral involved here.
: 2. choose three points on a circle and form a triangle. ask the probability
: of triangle is a right triangle.
|
J**********g
发帖数: 213 | 34 You are absolutely right. This is the first company that I got interview
from, and I did not prepare for brainteaser at all, and I knew only basic
statistics.
For the second one, I would guess zero, and this is definitely not the answer he was looking for. but I wanted to give an
vigorous mathematical explanation anyway (he definitely gonna ask me how I got it
after I told him the result, and I cannot say it's my guess).
For the third one, I tried two ways:
1. use chosky decomposition to transform to independent, then solve the
problem there.
2. after I got the first approach, I realized that we can solve it directly:
P{x>0|y<0}=P{x>0,y<0}/p{y<0}, we can calculate the top and bottom since we
have the joint density function if we know the covariance matrix, and of
course we can calculate p{y<0}, which itself is N(0,1)
possible third way. The reason I did not try the above two first, is that I
remember that that is some shortcut to translate it into some simple form,
but I simply did not remeber it, and thought I was supposed to answer the
question in that way. Anyway, I will work on it and hope to do better next
time.
【在 f*******y 的大作中提到】
: 楼主，不是我说，这些题目都fail说明你准备实在不足
:
: ask
: price
: probability
|
J**********g
发帖数: 213 | 35 answer to #1.
suppose the replicating portfolio consists of x bonds and y stocks. the
portfolio should have the same value at expiration as the call option. The
time zero value should be the value of call opition.
at time t=T
case 1: xB+yS=x85+y110=max(110-10)=10, execute the option
case 2: xB+yS=x90+y90=max(90-100, 0)=0, doesn't execute the option
solve for x and y and get x=-.4, y=.4, so the time zero value of the
porfolio (=the price of call option) is
-.4*85+.4*100=6 |
s*****r
发帖数: 2347 | 36 有个问题，这样分解之后的X Y都是standard normal，但是题目里没有提到X Y的mean
是0啊
【在 c******r 的大作中提到】
: En, I was treating the covariance to be 1/2 instead of 1/sqrt(2), but the
: idea applies similarly, let
: X = 1/\sqrt{2}(U-V)
: Y = U
: P(X>0|Y<0)=P(U>V,U<0)/P(U<0)= (1/8)/(1/2)=1/4
: I think in general for rho > 0, the result will be
: \frac{1}{pi}arctan(rho/\sqrt(1-rho^2))
|
b*******e
发帖数: 86 | 37 Is there some problem in ur answer?
I thought it should be
case 1: xB+yS=x90+y110=max(110-10)=10, execute the option
case 2: xB+yS=x85+y90=max(90-100, 0)=0, doesn't execute the option
the final answer is 6.8
【在 J**********g 的大作中提到】
: answer to #1.
: suppose the replicating portfolio consists of x bonds and y stocks. the
: portfolio should have the same value at expiration as the call option. The
: time zero value should be the value of call opition.
: at time t=T
: case 1: xB+yS=x85+y110=max(110-10)=10, execute the option
: case 2: xB+yS=x90+y90=max(90-100, 0)=0, doesn't execute the option
: solve for x and y and get x=-.4, y=.4, so the time zero value of the
: porfolio (=the price of call option) is
: -.4*85+.4*100=6
|
h*****i
发帖数: 1017 | |
