s******r
发帖数: 58 | 1 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
1300, you get 0, how much do you pay to play the game?
我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
2. There are many many tickets on the desk, there is one integer on each
ticket. You pick one ticket, the number is 100, what is the maximum integer
from the tickets on the desk. If you pick another ticket, the number is 200,
what is the maximum integer from t | s*******s
发帖数: 1568 | 2 GS竟然问这么NICE的题,赫赫
为啥我遇见的都这么BT
below
integer
200,
【在 s******r 的大作中提到】
: 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
: 1300, you get 0, how much do you pay to play the game?
: 我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
: 他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
: 2. There are many many tickets on the desk, there is one integer on each
: ticket. You pick one ticket, the number is 100, what is the maximum integer
: from the tickets on the desk. If you pick another ticket, the number is 200,
: what is the maximum integer from t
| d*j
发帖数: 13780 | 3 niu x
第二题怎么做？
【在 s*******s 的大作中提到】
: GS竟然问这么NICE的题,赫赫
: 为啥我遇见的都这么BT
:
: below
: integer
: 200,
| s*******s
发帖数: 1568 | 4 1 is digit option??
第二个用MLE,
prob of choosing a ticket is 1/N * 1{x<=N}, Then the estimator of N is maximum of x1 ... xn
below
integer
200,
【在 s******r 的大作中提到】
: 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
: 1300, you get 0, how much do you pay to play the game?
: 我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
: 他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
: 2. There are many many tickets on the desk, there is one integer on each
: ticket. You pick one ticket, the number is 100, what is the maximum integer
: from the tickets on the desk. If you pick another ticket, the number is 200,
: what is the maximum integer from t
| z****i
发帖数: 406 | 5 1是 digital option. the price is the risk neutral probability of S&P going
up to 1300, which is N(d2) in B-S formula | n******r
发帖数: 1247 | 6 do you have to assume Brownian motion for the S&P for this
why not sell the option now for $11/13, use this money to buy whatever share
you can buy for the 1x S&P500 index, when it hits 1300, sell them, you will
get $1 to payoff the option.
【在 z****i 的大作中提到】
: 1是 digital option. the price is the risk neutral probability of S&P going
: up to 1300, which is N(d2) in B-S formula
| z****i
发帖数: 406 | 7 The problem isn't quite clear... If it's a digital option, with fixed
expiration date, European style, then the price is N(d2), assuming black scholes framework.
if it's perpetual, the option pays $1 the first time it hits $1300, then the
price is just $2/13.
Please let me know if this is correct.
share
will
【在 n******r 的大作中提到】
: do you have to assume Brownian motion for the S&P for this
: why not sell the option now for $11/13, use this money to buy whatever share
: you can buy for the 1x S&P500 index, when it hits 1300, sell them, you will
: get $1 to payoff the option.
| a*****y
发帖数: 311 | 8
below
integer
200,
【在 s******r 的大作中提到】
: 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
: 1300, you get 0, how much do you pay to play the game?
: 我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
: 他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
: 2. There are many many tickets on the desk, there is one integer on each
: ticket. You pick one ticket, the number is 100, what is the maximum integer
: from the tickets on the desk. If you pick another ticket, the number is 200,
: what is the maximum integer from t
| a*****y
发帖数: 311 | 9 这是面什么位置的？
below
integer
200,
【在 s******r 的大作中提到】
: 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
: 1300, you get 0, how much do you pay to play the game?
: 我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
: 他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
: 2. There are many many tickets on the desk, there is one integer on each
: ticket. You pick one ticket, the number is 100, what is the maximum integer
: from the tickets on the desk. If you pick another ticket, the number is 200,
: what is the maximum integer from t
| z****i
发帖数: 406 | 10 the second problem, if the samples are from the uniform distribution [0,
theta], then the estimated theta would be the maximum of the samples, if we
are using MLE. so theta =100 if we just pull out one ticket, and theta =200
for the second time. but this estimation doesn't seem quite reasonable...
any ideas? | | | n******r
发帖数: 1247 | 11 Estimating a parameter with its sample analogue is usually reasonable.The
only thing made it looked strange in this case is the very limited sample
size.
If there is only one sample, the MLE estimators for mean, min, max are the
same.
For the max estimator,if the sample size increase to the populatoin size,
then the estimator converges to max of the population, therefore is at least
reasonable.
we
200
【在 z****i 的大作中提到】
: the second problem, if the samples are from the uniform distribution [0,
: theta], then the estimated theta would be the maximum of the samples, if we
: are using MLE. so theta =100 if we just pull out one ticket, and theta =200
: for the second time. but this estimation doesn't seem quite reasonable...
: any ideas?
| n******r
发帖数: 1247 | 12
scholes framework.
the
~~~~~~~~~~~~~~~~~~~~~~
$11/13?
【在 z****i 的大作中提到】
: The problem isn't quite clear... If it's a digital option, with fixed
: expiration date, European style, then the price is N(d2), assuming black scholes framework.
: if it's perpetual, the option pays $1 the first time it hits $1300, then the
: price is just $2/13.
: Please let me know if this is correct.
:
: share
: will
| z****i
发帖数: 406 | 13 You're right. sorry.
【在 n******r 的大作中提到】
:
: scholes framework.
: the
: ~~~~~~~~~~~~~~~~~~~~~~
: $11/13?
| s******r
发帖数: 58 | 14 麻烦大牛们写写答案，以鼓励偶贡献题目啊。每道题的过程和答案是什么呢？ | s******r
发帖数: 58 | | n******r
发帖数: 1247 | 16 第一题和第三题的思路是一样的
都是把自己假设成卖option的人，把在当前时刻去买相应的股票，用来对冲option的风
险，使得在执行option的时刻，无论股票涨跌，自己都有固定的收益
第三题，假设现在买delta份股票
如果涨，股票价格为$22，那么手里股票的价值是$22*delta,option损失$2,手里资产组
合的总价值22delta-2
如果跌，股票$18delta, option不损失，总价值$18delta
另两者相等，delta=0.5，即当前应该买1/2份股票来对冲option的风险，使得到了T时
刻，无论股票涨跌，自己手里都能有$9.假设利率为0，那么现在option应该卖$1,同时
再借$9就可以买0.5份股票。这个就是at money call option的最低价格。
具体参考John Hull chapter 11 binomial trees
【在 s******r 的大作中提到】
: 第二题要求说具体数字是多少
: 第三题怎么做？
| d*s
发帖数: 28 | 17 看来只要是关于高盛就能顶上来啊！！摩根就差那么一点，呵呵。（不好意思，我不会
做题，只能灌点这个了：） －－ 支持一下！ | s*******s
发帖数: 1568 | 18 我来补充一个,就是N层楼扔鸡蛋那个,现在有M个鸡蛋,要求通项解析公式,
当是一见到就知道肯定挂了,赫赫
【在 n******r 的大作中提到】
: 第一题和第三题的思路是一样的
: 都是把自己假设成卖option的人，把在当前时刻去买相应的股票，用来对冲option的风
: 险，使得在执行option的时刻，无论股票涨跌，自己都有固定的收益
: 第三题，假设现在买delta份股票
: 如果涨，股票价格为$22，那么手里股票的价值是$22*delta,option损失$2,手里资产组
: 合的总价值22delta-2
: 如果跌，股票$18delta, option不损失，总价值$18delta
: 另两者相等，delta=0.5，即当前应该买1/2份股票来对冲option的风险，使得到了T时
: 刻，无论股票涨跌，自己手里都能有$9.假设利率为0，那么现在option应该卖$1,同时
: 再借$9就可以买0.5份股票。这个就是at money call option的最低价格。
| d*j
发帖数: 13780 | 19 cft...
我的同学也挂在这个上面
我来补充一个,就是N层楼扔鸡蛋那个,现在有M个鸡蛋,要求通项解析公式,
当是一见到就知道肯定挂了,赫赫
【在 s*******s 的大作中提到】
: 我来补充一个,就是N层楼扔鸡蛋那个,现在有M个鸡蛋,要求通项解析公式,
: 当是一见到就知道肯定挂了,赫赫
| n******r
发帖数: 1247 | 20 真正理解两个是怎么用dp做的，三个还是可以推的
解释出来这么从2到3，那人还要你硬推M的公式那就是刁难了
开始一直觉得这都N年的老题了居然还问
现在感觉问的人suppose你就是看到过的，准备好等你把2的答案背出来，然后问3来看
你是不是懂了
【在 s*******s 的大作中提到】
: 我来补充一个,就是N层楼扔鸡蛋那个,现在有M个鸡蛋,要求通项解析公式,
: 当是一见到就知道肯定挂了,赫赫
| | | w**********y
发帖数: 1691 | 21
we
200
This is similar as one question in my previous interview with Bloomberg.
I think the MLE is only the first step.
The following question should be " How about an estimator by some scaled
mean (actually, 2*sample_mean) or median? Which is better?"
The last question is, any other estimators? Which one is better and how to
evaluate a statistical estimator?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Actually, the UMVU(uniformly minimum variance unbiased) estimator is (n+1)/n
*X_max. Somet
【在 z****i 的大作中提到】
: the second problem, if the samples are from the uniform distribution [0,
: theta], then the estimated theta would be the maximum of the samples, if we
: are using MLE. so theta =100 if we just pull out one ticket, and theta =200
: for the second time. but this estimation doesn't seem quite reasonable...
: any ideas?
| x**y
发帖数: 10012 | 22 我估计问这个问题的人可能自己不堪答案也不会做
不过没办法
【在 n******r 的大作中提到】
: 真正理解两个是怎么用dp做的，三个还是可以推的
: 解释出来这么从2到3，那人还要你硬推M的公式那就是刁难了
: 开始一直觉得这都N年的老题了居然还问
: 现在感觉问的人suppose你就是看到过的，准备好等你把2的答案背出来，然后问3来看
: 你是不是懂了
| n******r
发帖数: 1247 | 23 that's a nice extension of the problem and thanks for sharing
The book Statistical Inference by George Casella and Roger L. Berger pp311-
355 covers all the problems here
.
/n
【在 w**********y 的大作中提到】
:
: we
: 200
: This is similar as one question in my previous interview with Bloomberg.
: I think the MLE is only the first step.
: The following question should be " How about an estimator by some scaled
: mean (actually, 2*sample_mean) or median? Which is better?"
: The last question is, any other estimators? Which one is better and how to
: evaluate a statistical estimator?
: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| w**********y
发帖数: 1691 | 24
good reference.这本书基本上是很多学校数理统计的入门理论书.gigapedia上面可以
找到djvu版本的.(以前没有电子版,因为中国一直都卖36RMB一本..大家都懒的搞db)
【在 n******r 的大作中提到】
: that's a nice extension of the problem and thanks for sharing
: The book Statistical Inference by George Casella and Roger L. Berger pp311-
: 355 covers all the problems here
:
: .
: /n
| n******r
发帖数: 1247 | 25 手上这本就是39RMB的，纸张薄的可以看到反面的字，哈哈
【在 w**********y 的大作中提到】
:
: good reference.这本书基本上是很多学校数理统计的入门理论书.gigapedia上面可以
: 找到djvu版本的.(以前没有电子版,因为中国一直都卖36RMB一本..大家都懒的搞db)
| p*****k
发帖数: 318 | 26
isn't the maximum # of floors distinguishable with M eggs and
with the worst case of X droppings:
C(X,1)+C(X,2)+...+C(X,M)
where C are the binomial coefficients.
then solve the least X satisfying:
C(X,1)+C(X,2)+...+C(X,M)>=N
【在 s*******s 的大作中提到】
: 我来补充一个,就是N层楼扔鸡蛋那个,现在有M个鸡蛋,要求通项解析公式,
: 当是一见到就知道肯定挂了,赫赫
| w****j
发帖数: 6262 | 27 如果你连第三题都不会做，强烈建议你还是找几本书看看，稍微准备一下再出来投简历
。这样太浪费机会了，碰运气是不可能通过现在的变态面试的。
真的no offense，我自己也是菜鸟，也在挣扎，只是建议。
第三题是最基本的b-tree的option定价，核心就是概率没有意义，要计算risk-neutral的概率是
0.5，所以option价格是1。
【在 s******r 的大作中提到】
: 第二题要求说具体数字是多少
: 第三题怎么做？
| M*****y
发帖数: 666 | 28 For question2: assume uniform dist.
if you use MLE, then P(X=k)=1/N where 1<=k<=N
So 1/N is max where N is min at N=k, here is k is 100, then max N=100; if k
is 200, then max N=200
However, if you use MME to estimate the max:
Xbar=mu, and we pick one number and get X=k, Xbar=k=mu=(N+1)/2
So if k=100, then max N=199
if k=200, then max N=399
below
integer
200,
【在 s******r 的大作中提到】
: 1. S&P500 is 1100 now, if it moves above 1300, you get $1, if it moves below
: 1300, you get 0, how much do you pay to play the game?
: 我说entry price是 probability that S&P500 is above 1300. 但不知道是什么.
: 他给了hint是用Black–Scholes formula,可是我还是不知道怎么用.
: 2. There are many many tickets on the desk, there is one integer on each
: ticket. You pick one ticket, the number is 100, what is the maximum integer
: from the tickets on the desk. If you pick another ticket, the number is 200,
: what is the maximum integer from t
| d*s
发帖数: 28 | 29 楼主应该是做research的，本来就应该多问research相关的啊，你看CS申请developper
职位的，都问C++,JAVA,研究的
projects什么的，没有用什么binomial tree/finite difference, risk-neutral
measure之类高深的问题去为难人家吧？
（我是外行，说不对别拍～～）
neutral的概率是
【在 w****j 的大作中提到】
: 如果你连第三题都不会做，强烈建议你还是找几本书看看，稍微准备一下再出来投简历
: 。这样太浪费机会了，碰运气是不可能通过现在的变态面试的。
: 真的no offense，我自己也是菜鸟，也在挣扎，只是建议。
: 第三题是最基本的b-tree的option定价，核心就是概率没有意义，要计算risk-neutral的概率是
: 0.5，所以option价格是1。
| e****q
发帖数: 1668 | 30 I agree with this.
share
will
【在 n******r 的大作中提到】
: do you have to assume Brownian motion for the S&P for this
: why not sell the option now for $11/13, use this money to buy whatever share
: you can buy for the 1x S&P500 index, when it hits 1300, sell them, you will
: get $1 to payoff the option.
| | | w****j
发帖数: 6262 | 31 你能不能讲讲，三个鸡蛋怎么推呢？
【在 n******r 的大作中提到】
: 真正理解两个是怎么用dp做的，三个还是可以推的
: 解释出来这么从2到3，那人还要你硬推M的公式那就是刁难了
: 开始一直觉得这都N年的老题了居然还问
: 现在感觉问的人suppose你就是看到过的，准备好等你把2的答案背出来，然后问3来看
: 你是不是懂了
| w****j
发帖数: 6262 | 32 能解释一下为什么呢？多谢。
【在 p*****k 的大作中提到】
:
: isn't the maximum # of floors distinguishable with M eggs and
: with the worst case of X droppings:
: C(X,1)+C(X,2)+...+C(X,M)
: where C are the binomial coefficients.
: then solve the least X satisfying:
: C(X,1)+C(X,2)+...+C(X,M)>=N
| n******r
发帖数: 1247 | 33 pcasnik老大都给出通解了，等他来解释吧，我也听听
【在 w****j 的大作中提到】
: 你能不能讲讲，三个鸡蛋怎么推呢？
| S*********g
发帖数: 5298 | 34 Assume F(X,M) = the # of floors can be solved with M eggs and X tries
we have F(X,M) = F(X-1,M-1) + 1 + F(X-1,M)
(This is so because we want to try first on the (F(X-1,M-1)+1)-th floor. If
it breaks, we have M-1 eggs and X-1 tries, otherwise, M eggs and X-1 tries
define d(X,M) = F(X,M)-F(X,M-1)
d(X,M) = F(X-1,M-1) + F(X-1,M) - F(X-1,M-2) - F(X-1,M-1)
= [F(X-1, M) - F(X-1,M-1)] + [F(X-1,M-1)-F(X-1,M-2)]
=d(X-1,M) + d(X-1,M-1)
notice that
C(X,M)-C(X-1,M)=C(X-1,M-1)
if C(X,M)= X*(X-1)
【在 w****j 的大作中提到】
: 能解释一下为什么呢？多谢。
| w****j
发帖数: 6262 | 35 牛人呀，
不过最后一步，类比就说d(X,M)就是C(X,M)，是不是略有点不特别严格？
If
tries
【在 S*********g 的大作中提到】
: Assume F(X,M) = the # of floors can be solved with M eggs and X tries
: we have F(X,M) = F(X-1,M-1) + 1 + F(X-1,M)
: (This is so because we want to try first on the (F(X-1,M-1)+1)-th floor. If
: it breaks, we have M-1 eggs and X-1 tries, otherwise, M eggs and X-1 tries
: define d(X,M) = F(X,M)-F(X,M-1)
: d(X,M) = F(X-1,M-1) + F(X-1,M) - F(X-1,M-2) - F(X-1,M-1)
: = [F(X-1, M) - F(X-1,M-1)] + [F(X-1,M-1)-F(X-1,M-2)]
: =d(X-1,M) + d(X-1,M-1)
: notice that
: C(X,M)-C(X-1,M)=C(X-1,M-1)
| S*********g
发帖数: 5298 | 36 I omitted one step.
You can use boundary condition to get the final result.
【在 w****j 的大作中提到】
: 牛人呀，
: 不过最后一步，类比就说d(X,M)就是C(X,M)，是不是略有点不特别严格？
:
: If
: tries
| p*****k
发帖数: 318 | 37 regard the egg-dropping(:P) problem, one can get the bound by
considering how many configurations the test results will be.
same notation. note for each dropping, either egg breaks
(denote as "1") or not ("0"). so you end up with an X-element
array (worst or at most X tests) with at most M (total # of eggs)
"1"s, so total of:
N_max = C(X,0)+C(X,1)+...+C(X,M)
results, thus one can at most distinguish N_max floors.
this is of course only a bound. one needs to construct a strategy
to actually sa |
|
