\usepackage{soul}

\hl{contents to be highlighted}

1)For American option, when risk free interest rate increase, will it
increase the possibility of early excises?

2)For best of two options, you buy one option, which will give you the best
payoff between two underlying options. For example,for a best put option,
two stocks A (A0 =100) and B( A0=100), strike =100, After time T, A became
80, B became 110, then you got 20, if A became 80, B became 70, you got 30.
The prices of put option for A and B are 4 and 3, respectively. Please
pricing the best two option, what's bound of this option? When the
correlation between A and B change, how will it affect the option price?

3) \sum (N from 0 to infinity) N^2*a^N. a = constant

4) The variance of \integration ( t from 0 to T) sigma(t)dW .

5) When the volatility increase, how the Gamma will change?

6) How to sort?

1. dX_t = exp(-rt)dW_t, what's the variance of X_t?

2. stock price = 100, will be 120 w.p. 0.5, and 70 w.p. 0.5, what's the
price of an at-the-money option?

3. what's the algorithm to generate normal r.v. and exponential r.v.?

4. for what option you prefer to use finite difference, and what prefer
using Monte Carlo?

5. How to detect a loop in a link list? (totally lost@@)

6. 我不大会C++，就往我会的上面扯，我说我听过bubble sort和binary search，他就
问了我下这俩的复杂度

7. 骰子题，应该是经典题了吧。 最多可以掷三次，自己决定stop与否，payoff 是最
后一次掷的点数。 what's the price for offering this game?

8. 其他的还问了一些stochastic volality 和 short-rate model。

发信人: sosohui (confused), 信区: Quant
标 题: 问个简单的问题
发信站: BBS 未名空间站 (Fri Jun 11 17:43:40 2010, 美东)

you have a digital clock ( no seconds ) that you randomly look
at once at a time defined as t1 and then keep looking until
it turns to the next minute defined as t2.

a) what is the expected value of t2-t1 ( i.e : mu ) and variance of
t2-t1 ( i.e :sigma squared )

b) what is mu plus or minus 2*sigma and what does it mean ?


理解为t1和t2是两个独立的U[0,60]吗？还是别的？b是说confidence interval吗？谢
谢。

1. dX_t = exp(-rt)dW_t, what's the variance of X_t?

2. stock price = 100, will be 120 w.p. 0.5, and 70 w.p. 0.5, what's the
price of an at-the-money option?

3. what's the algorithm to generate normal r.v. and exponential r.v.?

4. for what option you prefer to use finite difference, and what prefer
using Monte Carlo?

5. How to detect a loop in a link list? (totally lost@@)

6. 我不大会C++，就往我会的上面扯，我说我听过bubble sort和binary search，他就
问了我下这俩的复杂度

7. 骰子题，应该是经典题了吧。 最多可以掷三次，自己决定stop与否，payoff 是最
后一次掷的点数。 what's the price for offering this game?

8. 其他的还问了一些stochastic volality 和 short-rate model。

difference between pointer and reference
how to switch two variables without the third one
integral of 1/sinx
expectation of W^6 (using Ito's lemma)
when do you get positive theta? intuitive explanation?

刚面了，估计没戏，问的differential equation都n>10年没有用了，faint，一点也不
fit自己背景：

First series of question about C++:
1. implement a sorted list: what are the interfaces you would like to design;
2. how to make both insertion/remove efficient? which data structure/
algorithm?
3. how to implement the ++ operator of the iterator in this data structure (
if you get 2 correct);

Second series of question about OE:

solve equation y'' + x*y = 0, where y is a function of x.

Asked many questions based on this OE, such as what is the solution? shape?
how to solve numerically? what
type of conditions you need to find a unique solution? After you figure the
shape of the solution, then asked
many properties of the solution.

两个 Goldman Sachs 题：

1)How to price a derivative which pays S(T)log(S(T))? suppose S follows
geometric brownian motion

2) X~N(0,1), F(x) is cdf of X, Y~N(a,b), what is E(F(Y))?

跟福州客学的。

鱼切块，放入味精，一点糖，料酒，姜片，葱段，干辣椒，当归，枸杞子，冻腌一段时间。

水烧开后，放入鱼盘，蒸15分钟。

鱼蒸好后，淋上蒸鱼耗油。

烧油至滚，浇到鱼上，浇时候滋滋冒烟最佳。

跟福州房客学的。

鱼切块，加入盐，味精，姜末，五香粉，白酒（不是料酒），腌半个钟头。

鱼在煮之前加入淀粉拌。

加油入锅，加入葱头，生姜炒，加盐，再加水，水烧开后加入鱼。

煮水滚几下就好，不要太久，出锅前加胡椒粉和醋，出锅。

1)How to price a derivative which pays S(T)log(S(T))? suppose S follows
geometric brownian motion

2) X~N(0,1), F(x) is cdf of X, Y~N(a,b), what is E(F(Y))?

发信人: skydoor (海阔天空), 信区: JobHunting
标  题: 高盛onsite9小时9人车轮战归来
发信站: BBS 未名空间站 (Sat Apr 24 02:06:12 2010, 美东)

三流学校fresh Phd, 莫名其妙的被别的recruiter投的developer职位, 我自己都不知
道怎么居然被高盛看上了, 前面两轮电话面经已经发过了, 今天onsite.  我此前一天
拿了Bloomberg offer, 今天面试高盛, 感觉跟Bloomberg比起来, Bloomberg完全不是
一回事啊. Bloomberg总共2小时面试, 2个人45分钟技术面试, 一般manager都不会问技
术问题, 更不谈HR了. 高盛今天从早上8点进门开始到下午5点出门结束直接被送到飞机
场, 9个小时连续见了9个人, 每个人45分钟面试. 住在曼哈顿, 5:30就起床, 轮渡到新
泽西,  新泽西building见了7个, 然后轮渡到曼哈顿的building见了俩个.  前天住酒
店没休息好, 中间面到第三个的时候差点呕吐,还好及时调整. 一整天靠两杯咖啡维持,
在一个屋子里面等着不同人一个个来面试你, 全程还要保持微笑, 讲自己的research,
讨论题目, 时刻纸上写程序, 简直就是脑力和体力的双重折磨. 还好会议室外面就是
自由女神像, 感觉很是那么一回事.

整体而言, 1/4他们在吹牛, 1/4在讲我的research, 1/4在谈技术写程序, 1/4我在问问
题, 基本没有特别准备, 所有的准备都是平常general的准备. 写程序的题目都很简单,
版上都有, 基本也就写binary search的这个级别的程序, 有一个稍微难点, 但是也可
以handle, 个人觉得要求快, 要准确. 其他题目涵盖数学, 概率, brain teaser, C++,
Java, 线程, 算法等, 都很常见, 关键要熟练. 

第一个人, 老中, 这个面的最差, 因为才起来, 没进入状态. CS 背景, 问了俩数学题
目, 翻硬币之类的, 没做好, 感觉要挂了, 然后开始闲聊, 问为什么选金融行业, 然后
问C++, hashmap和map的区别, hash function如何解决conlision, 问了几个sorting题
目, 没答好, 然后我就开始问他问题, 问了10多分钟, 感觉像我在面试他.

这个之后下一个来中间空白了将近20分钟, 感觉是不是第一个没答好要被kick out了,
及其郁闷, 但是一想怎么着中国人都没这么mean, 谁知道这个后面的就感觉很好了.

第二个人, 老中, CS背景, 高盛工作了8年, 本科毕业就加入了, 听英语看样子是ABC或
者早期移民, 主要聊他做的事情, 一个人在那里狂说, 我就随便插几句附和, 他很high
的样子, 问我有什么idea, 我就闲扯, 后来问我怎么solve一个问题, 我没回答, 说没
有这个background, 他说没事, 我刚来的时候也没有, 然后聊了几个sorting, 几个
multithreading的问题, 我都答的还对, 就说, I am confident about your
knowledge, 我也心安了. 反正感觉他对我还算满意, 可能前面他吹牛的时候, 我
response的让他感觉很爽.

这个时候突然开始不舒服, 要呕吐.

第三个人, 老美, CS背景, manager, 一来就开始开始吹牛, 讲自己做什么, 然后问我
research, 我就讲research, 然后说问你C++, 我说好, 他问, 什么是public, private
和protected, 我狂倒blablabla....然后问, 什么是public inheritance, private
inheritance 和 protected inheritance, 才知道是为了铺垫这个, 然后问什么是多重
继承, 然后还问了几个C++, 然后给了个题目, 一个数mising怎么找, 写程序, 我说求
和啊, 然后又说如果很多数, 会overflow, 怎么搞, 我说binary search, 我写到一半
的时候, 他叫停了, 说对的. 最后小秘过来说他有电话, 他问我是否还有问题, 我又问
了他10多分钟, 他没走的意思, 我问完了还要我问问题, 我又问了一个, 这让我感觉还
不错.

第四个, 老美, finance背景, 这个基本就是鬼扯, 主要讲我的research, 要把他们这
样的人忽悠懂还有点困难, 然后问我有啥问题, 又跟他鬼扯了20分钟.

第五个, 女老美, finance 背景, 同上, 基本就是鬼扯, 讲research, 问我为什么选择
finance, 然后问我有啥问题, 我把问上一个的问题又重新问了一遍.

第六个, 台湾人, CS背景, 带我去吃午饭, 边吃边聊, 然后问我C++和Java的区别, 线
程和进程的区别, 还有其他的CS问题, 然后给个算法程序我写, 求一个array的最大的
sum的subset, 我写给他, 他说对的.

这个还没面完的时候, 第七个人已经进来了

第七个人, 老美, CS背景, 讲research, 然后他开始吹牛, 我们对吹, 对问问题. 后来
快结束的时候, 居然告诉要到另外一个building去面试另外俩人, 我倒, 我一开始就没
有拿到schedule, 都不知道他们要这么安排.

然后从新泽西轮渡到曼哈顿, 见到第8个人,

第八个人, 老美, CS背景, 讲research, 问C++, 给题目写程序, 写到一半,说对的, 不
用写了, 然后给个没见过的题目我讨论, 应该是他们实际的题目, 需要用到radix
sorting, 我一百年不知道这个, 讨论得当时吓的汗都出来了, 还好东搞搞西搞搞给了
满意的答案. 其实, 也很简单.

第九个人, 老美, CS背景, 开始吹牛, 然后我讲research, 然后讨论C++和java的
memory management,知道的不多, 瞎扯,  还问了其他很多C++问题, 包括virtual
function, smart pointer, new delete, 给了个brain teaser, 25匹马那个. 然后问
我的unproductive project, 为什么读Phd, 未来5年想干啥, 以及很多乱七八糟的问题
. 然后要我问他问题, 我就问贝.

然后出来, 专门有车送到了飞机场, 现在回家了. 接我的车是林肯, 送我的车是凌志,
酒店在曼哈顿, email写的300刀一晚上, 感觉跟我们农村100刀的也差不多.

整个过程, research讲了5,6遍, 说的我都要晕头了.

总结

1 高盛的人, 完全不是一个档次的, 无论是思维方式还是行为举止, 讲research一讲就
懂, 而且还能提出很多问题, 基本上比系的faculty水平都高.

2 没有阿三, 真好, 反而三老中;

3 问他们问题很重要, 问题问得好对方明显表情就不一样了, 问的不好就气氛很尴尬,
比如我问, why do you enjoy your work, 哇, 对方就来劲了, 开始吹牛. 坏问题我问
了一个, 比如其中一个谈到group人员的diverstiy, 我问了, what's the difficulty
to work with others, 气氛就很尴尬, 我就后悔了, 这不明摆着要对方说别人坏话么?
于是我赶紧问了另外一个, what's the biggest fun, 气氛就好了一些.

4 交流很重要, 他们自己都说, 我们这么多人见你, 就是看你是否fit我们这个group,
是否可以一起work. 个人感觉交流不光是英语, 当然英语不好肯定不行, 随便I am
sorry几下就要挂了,  交流更重要的是如何response对方说的东西, 感觉像说相声, 对
方逗哏, 我捧哏, 我要不停的right, good, interesting, excellent, wow, 如果中途
接上话茬, 他们明显两眼放光, 如果我不response, 对方明显语速放慢;

5 程序一定要会写, 但是, 都不难, 版上那些google, ms的变态的描述都描述不清楚的
算法题, 绝对不会出现;

6 金融知识完全不重要, C++很重要, 不过如果C++不知道, 可能电面早就挂了.

7 HR没有出来搅和


猎头说底薪100k, 说下周出结果, 这已经不重要了, 当然如果给我offer, 我肯定据
Bloomberg.

发信人: zhucai (zhucai), 信区: Quant
标  题: 被jane street拒了，发面经攒人品吧
发信站: BBS 未名空间站 (Thu Feb 25 15:53:02 2010, 美东)


昨天面了第2轮电面，今天就发了拒信，效率真高啊。。

第1轮：

几个心算题： 444+889, 20,000-22, 11%*56, 42^2.

1到100所有奇数加和是多少；

认5次fair coin, 扔到的head个数为偶数的概率是多少；

扔4次fair coin, exactly 3 heads的概率， at least 2 heads 的概率；

扔两次dice, 第1次大于第2次的概率；

扔12次fair coin， 扔到的head个数为偶数的概率是多少；

play a game, 扔两个10-faced dice, 取和。 两个人猜，猜的数离实际扔出来的数最
接近的赢。 问你应该先猜还是后猜，（后猜的人不能跟前一个人猜相同的数）， 什么
strategy. 假设你的对手足够smart.




第2轮：

1. 假设一个treasury chest的value符合$0-$1000的均匀分布。你bid，如果它的实际
价值低于你bid的值，那你就可以以你bid的值买下它，然后你可以以它原来价值的1.5
倍卖掉。 问你应该怎么样bid？ （这个我用积分算期望的，然后说不该bid，她（对，
是个女的）说，如果不用积分，你该怎么样intuitive得解释，比如说，假设你在对一
个小学生讲这个问题。。然后我就傻了）

2. two towns, A和B， 1000 miles apart. 现在有3000个苹果在A地。 开一个卡车，
最多可以装1000个苹果，每开1迈掉一个苹果，问最多可以运多少个苹果过去。

3. 经典问题。扔一个die， 每一个点给$1, 问fair game的话， 出多少钱玩这个游戏
。 如果允许你玩第2次呢？ 什么strategy.

4. 扔两个dice， 两个值的积是一个square number的概率。

5. 扔一个die若干次，直到总和严格大于22，问最后的结果mostly likely会是多少？
（完全没有idea怎么做。。。）

6. 3^100有多少位。 给一分钟，估出上下界来（要你的confidence level为90％），
她在一边计时。


再说一下，所有的问题都要求你很快，并且要你说理由而不只是答案。 面试过程中很
push，不给你任何喘息的机会。。 每一个问题答完后都问你how confident are you.


祝大家好运吧

发信人: daj (肉丝炒饭--小吵肉fan), 信区: Quant
标  题: 总结一下
发信站: BBS 未名空间站 (Sat Apr 24 21:07:00 2010, 美东)


有问题回帖问吧， 版上大牛也会帮忙的， 比单单问我一个小虾米强多了


先从大牛的帖子开始吧， 还有个时间的定位

发信人: twosigbama (图么丝？图西格巴马！), 信区: Quant

标  题: Re: 最近某大行又砍人砍得血肉模糊

发信站: BBS 未名空间站 (Mon Mar 29 23:33:28 2010, 美东)

Because lehman and bear are gone.

Goldman, Morgan Stanley, JP Morgan, Merrill/BOA are clearly the best four.

Credit Swiss, UBS, DB, Citi fight for the rest. These guys are second tier

because they dont have the ball to pay ppl as early as first tier firms do.

UBS is top 5 because clearly it is not top 4.


当时看完大牛的帖子， 自己算了一下， 上面8个公司除了两个一直没有理我， 其余六
个我都总共有了15次左右的面试， 但是还是没有offer, 第一次感觉着急。自己一直想
去大银行做quant，感觉很多职位都面过了， 以后再也没有机会。 后来， 四月份从这
几个公司又来了4个面试， 幸运的抓住了一个，有了offer 现在在 background check.



面试经历：


1 GS面试  还是需要 network, 基本上都是学校和同学的关系找的。 他们很挑人， 我
这样的烂人基本没希望， 就算你面试问题答得好。 不管怎么说， 去 MSCF 还是有价值
的， 我一个进去的同学也常说， GS 里面经常看到 MSCF的简历。

2 MS 网投还是很有用的， 特别是伦敦的职位，一投一个准， 感觉那里的HR比较负责，
或者就是他们海面。我自己的英语听力可能不行， 听伦敦口音有心理障碍。。。。

以上 GS  MS 除非特别牛人， 否则慢慢等吧 一轮电话 + 两轮 onsite 每次间隔2--3礼
拜， 去 on site 不给钱 一般。或者来个多轮 phone interview.


JP morgan   UBS 从来不理我， 一直到最后


3 BOA 可能需要多多和他们的 HR联系， 看看他们的 facebook  linkdin 什么的

面过他们的 risk , 2 front desk quant, 还有一个 NYC PHD Superday, 呵呵 版上几
个大牛也在那里， HR说收集了几百个简历吧， 那一次选了7个人 super day, 6位同胞
， 都是自己人在 PK.   mortgage desk quant 面试的不错， 问我去不去 atlanta ..
. 我听成加拿大， 说不去， 现在还是有点后悔的。 risk 那个position， 电话面试的
人说 你的表现很不错 看你的简历也很不错， 可以轻易的进入 quant group, 你确定你
想来这里吗?  我犹豫了好一会， 才很不坚决的说愿意， 因为可以使简历好看。。。就
没有回音了 看来是个愚蠢的回答。


credit suisse 和 DB 只面过一次， CS 面得不错，回信说 positive, 没消息了， DB
呵呵， 面试风格是 S&T 那种， 哎， behavier + market, eurodollor future, sig
h ... 我以为是 euro/dollor  这个没办法


citi 嘛， 呵呵。 从这里开始 到这里结束。 第一个大公司面试就是他的， 最后一个
面试就算是他的吧， （其实是MS, 我说不用面了， 我接受了其他的offer）。 找到工
作的感受就是， 顶头上司看上你， 面试问题全答对， 就差不多了， 但是主要是上司
看上你， 帮你吹风， 其他的小兵 大头头 也就都没什么大问题了。 顶头上司先面试，
面完了以后随后来的四个小trader 人人 nice, 很基本的 greeks  option profolio
的问题，第二轮见senior， 就是基本的背景 + 闲聊， 当时有个 co head of this gr
oup, 说我的编程很弱， 确实是事实，后来也就这么过去了 。 电话给 offer 时候，
告诉我录用的原因， 不只是上两个， 着重强调了 他们延续了录取 CMU student 的传
统， 感谢啊。

说起citi, 另外一件事情就是， 找 intern的时候， 我已经手里有一个 offer 了， 还
没有接受，  citi 招人的 MD 想要叫我去 intern onsite interview，  后来又打电话
给我， 直接说他知道我手里有选择， 不想 ruin 他和 CMU 那个 program director 的
关系, 所以， 他极力劝我不要去啦。 我还是坚持要去， 面完了 很快收到拒信。 至于
他怎么知道我有选择的， 呵呵， 猜猜看吧。 这个反映了学校和学生的利益冲突， 学
校要的是 100% placement , 学生要的是 best offer. 大家以后有 offer, 不要早早的
报告学校。


另外其他的大公司的面试我都接了， 比如 PIMCO  BNP 等等。 其他的如 PNC  SEC bl
oomberg 两房的面试 都直接拒掉了， 因为知道拿了offer也不会去的，后来也面了什么
s and p  reval quantifi 之类的 NYC local 小公司 当做练练手  这些小公司的面试
都是学校的 resume book 找来的， 数量还是不少的。


个人背景：　

很一般很一般的学校 数学 PhD +  MSCF,  编程很弱。 其他的数学  金融还凑合了

猎头：

除非大牛人， 否则猎头推荐的职位拿到面试很容易, 但很难有offer。用他们练手倒是
很不错。市场上 牛校的数学 Ph.D 最受欢迎， 大公司的猎头通常都有自己独有的信息
， 小公司基本上有的都是所有公司都有的职位

MFE 选择问题：

UCB  NYU  CMU CORNELL吧， 其他的学校 如果career service 差， 你什么都自己找，
非常难。

投简历:

快毕业的人， 不管是 full time,还是intern, 官网看到合适就投吧， 别看有的 inte
rn要求时间内毕业什么的， 其实就算你已经毕业了， 有的公司根本不管。intern结束
后， 如果你有 return offer, 可以马上工作的， 理论上可以， 具体还要看 HR 给不
给办。


面试题目

没分类， 大家凑合看吧 烂大街的题目 以及和简历有关的technical Q  直接忽略了


Heard on The Street: Quantitative Questions from Wall Street Job Interviews



A Practical Guide To Quantitative Finance Interviews by Xinfeng Zhou

Quant Job Interview Questions And Answers by Mark Joshi

这三本书还是需要看的


digital call option 的 vega， how to hedge a digital call

MBS convexcity 和 它的curve

a vector, look for its median, 面试人给出的提示是  用quick sort 的 idea

exp distribution. default intensity , survival probabilty, inverse CDF to ge
nerate RV,

为什么stock price 用 log normal

change of measure, change of numerie 大体意思， 原因

two normal, uncorrelated  and independence, 还要举反例

brownian motion and heat equantion 关系， 怎么理解这个东西

poission distribution, no memory property to prove sth

BS formula, all kinds of questions, the delta hedging idea behind it, positi
ve convexity of call

time series analysis questions, what is stationary process, how to make it t
o a stationary process, ARMA Garch  stochastic vol

variance reduction method for MC

生日问题， N个人， 生日不同概率，函数增减  然后 estimate prob >1/2,  N=?   t
ake log 需要用 一阶泰勒展开

time integral of W_t


sqrt(37) = ?

a B_t , reach  -3  or 5 , probability to each 3 first ?  what if a difted B_
t


100! 有几位数 ？

C++ 里面     class A;  A a;  Class  b=a;   调用了什么？ 为什么不是 assignmen
t operator.

C++里面的， first created last destroyed,  给你一具体题目考察知不知道这个

x follows f(x), y follows g(y), x y independent,  x+y  follow what ?

forward price, how to show this by replication

an Asian forward contract, price it using replication

use MC to estimate Pi

Excel 表格里面， 比如某个列的名字是  AZ， 写一个程序， 返回是第几列

x  y  z follows iid  U[0,1], expected value of min/max [x,y,z]

bond duration and convexity 各种问题

inverse a char array

solve  x'' +x' +x=0

newton's method  各种问题公式啊 推倒之类的， 以及类似的 切线法

各种 greeks, 定义， 画图  知道什么样子的

how to hedge a digital option

什么是 measure, 为什么有不同的measure


risk neutral valuation 你怎么理解的

call on index VS call on N stocks   , index 由 N stocks 组成的

各种 sorting algo

1000 int , 范围是 0---5000,  排序

put call parity 及相关， 和 forward 有关， 还有和 non optimal to exercise am
erican call 有关

matlab里面怎写一个匿名的函数

写一个 copy constructor  assignment operator , class 里面包含指针的， 比如建
立一个 linkedlist. 然后怎样 hide its structure

convex hull ,  给你许多点， 找出

confidence interval 相关的， 给他一个  95%  1.96  一般就可以了

hull white model 各个参数的意思， 怎样 calibrate

CDS 怎么定价， 各种情况下， 怎么变化， 比如 recovery rate 上升 或者 default
probability下降

CDS A : 200bps  , CDS B : 100bps, 你是买一半A 一半B, 还是买一个 index 由 A+B
组成  150bps

MBS 当 interest rate vol 上升， 会怎样

Suppose you have a portfolio of 100 bonds, each with a 1% yearly default ra
te.  What are the odds that no bonds in the portfolio default in a given yea
r?  Estimate this to the first digit.  What happens if there is correlation
between the bond defaults?



http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign#Derivat
ion_of_the_principle_of_differentiation_under_the_integral_sign

这个东西， PIMCO  GS 都问过， 大体的证明思路


一个排序好的 int array, 给你一个数 n , 找出 say  100-k 在不在这个数组里面

x y iid follows U[0,1]  P(x*y < 1/2)


rand(5) 可以随机等概率生成 1 2 3 4 5     用这个 generate  rand(7)

发信人: tempone (jane), 信区: Quant
标  题: binomial model again
发信站: BBS 未名空间站 (Sat Apr 17 01:58:55 2010, 美东)

u = exp(sigma *sqrt(delta_t))
d = exp(-sigma *sqrt(delta_t))
p = (expt(r * delta_t) - d) / (u - d).
S_0 = 1;

At step n, whats the variance?

I follow the suggestion of this board and use the variance definition:
a node at nth is u^kd^(n-k). the probability is C_n_k * p^k * (1-p)^(n-k)

the expected stock price is exp(r * n *delta_t)
variance is sum over 0..n (C_n_k *p^k *(1-p)^(n-k) * (u^kd^(n-k)^2 - expt(-2
*n * delta_t) and I fursther simply this to:

(p*u^2 + (1-p) * d^2)^2 - expt(2*r*n*delta_t)

but after that I dont know how to further simply. I think the final anser
should be sigma^2 * T, is that?

can anybody help to give a hint how to further simply to get the solution?

发信人: Jadeson (Jadeson), 信区: Quant
标  题: 问两道面试题
发信站: BBS 未名空间站 (Wed Apr  7 13:03:48 2010, 美东)

很奇怪的题目，因为不知道提问者到底要考什么，要命的是两道题目似乎是他们共有题
库的，已经分别被问过两次了。

1。假设underlying=100，问90和100的put哪个的风险大。

第一次是被GS的risk部门问，第二次是被一个HF的傻B trader问（后来查了，此人原来
在GS做过）。

这道题实在问的莫名其妙，我看着很迷茫。哪位能解释一下。

2。假定USD/EUR的过程是

d p = p(r_u-r_e)dt+p*sig dW

那么按照Ito公式， EUR/USD的过程则应该是

d q= q(r_e-r_u-sig^2)dt+q*sig dW

但是如果单考虑EUR/USD的过程，类似于USD/EUR，就该是

d q=q(r_u-r_e)dt+q*sig dW

问怎么解释。MS和BB都问过这道题。

我的感觉其实没什么好解释的：作为derivative pricing，任何定价都是在risk
neutral底下的，U/E和E/U都是可交易的产品，所以不管你的drift是什么，最后都可以
用侧度变换，化为r_u-r_e。

但是两家公司都不满意这个解释。不知道他们想问什么。

发信人: HiThere (HiThere), 信区: Quant
标  题: questions
发信站: BBS 未名空间站 (Thu Apr 15 22:14:32 2010, 美东)

最近申请C++程序员,被锯,C++没问题, 可被问了写FIANCE的问题,不清楚, 贡献出来,不
会的,有人回
答吗?

1.DURATION, 这个俺知道.
2.calculate MSFT forward price
  current pirce * ( 1+ r)^n - dividend discount by r ?
3.option pay off graph, 这个俺知道.
4.option greeks,这个俺知道 how delta change with moneyness, draw graph,
skewness, don't know.
5.interest rate swap, how to calculate fixed rate? it said my calculation
was wrong.
6.option free bond pricing. discount cash flow by using rate on rate
curve.
7.tips--how to price?

1. What's the distribution of the stopping time T=min{t>=0: W(t)>100}?
   
2. 船里有人, 人手里有东西, 东西扔下去, 沉了, 然后问, 水面怎么涨, 船水位怎么涨?
   
3. 如何求sqrt, 我说牛顿算法, 和binary search, 然后问我, binary search 有什么
   问题, sqrt(35) 和sqrt(37) binary search都一样么? 怎么改进? 用牛顿和binary search有什么区别, 分别什么时候用.
   
   如果是让我们算sqrt(35)或sqrt(37),是不是可以这样心算？
   sqrt(37) = 6+x = sqrt(36 + 12 x + x^2)
   12x + x^2 = 12 x = 1 ==> x=0.08
   so, sqrt(37)=6.08
   我计算器算的是6.083
   
4. 绑匪绑架了女儿, 要从一个杂志里面cut paste一个note, 写一个function, 判断是
   否可以写这个note, 两个input, 一个杂志的string, 一个是note的string, 返回bool.
   (可以构造一个hash，count每个character出现的次数。要求对于每个character，
   note的次数要<=杂志的次数。)

发信人: weekendsunny (醉生梦死), 信区: Quant
标  题: 总结: Perpetual Binary Barrier Option
发信站: BBS 未名空间站 (Wed Mar 31 22:38:09 2010, 美东)

Zhucai mm今天说的那个经典问题，说现在的股价是S=$80， 有个barrier是K=$100，
第一问: B>S.  一个option， paysoff $1 when the stock hits B. 问价格是多少。
第二问,如果是B<S呢？

看完了资料,总结.欢迎讨论交流
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
大部分人同意的做法:
现在买1/100只股票,stoppingtime的时候,payoff一样.所以定价应该是80*1/100=$0.8.
咋看起来没问题.
那问个问题哈,如果我今天replication的portfolio是1/50股票-$1呢,payoff还是一样.
那这个portfolio的定价是0.6.当然你还可以制造出无数个不同的replication的
portfolio.也就是market不是non-arbitrage的,除非..除非你多给点条件..

加一个条件:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
看heard上面的question2.3,他实际上加了一个条件:
(原条件)如果S(<K)向上 hit K=$100, knock-out with $1;
(新条件)如果S向下 hit 0, knock-out with $0;
然后结果就对了.non-arbitrage了
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
如果不加这个条件:
当然了,risk-neutral pricing还是能算出结果的,其实就是假设stock
price是GBM,然后dS/S=rdt+sigmadW,算E(exp(-r*tau)),tau是hit K的stopping time.
这个时候,如果假设r=0,lnS的drift是-0.5sigma^2,那就等价于求P(tau<\infty).这个
是小于1的,因为你drift是负.
这个结果和加上了新条件后的结果一样
这个结果和heard上解带两个boundary条件的PDE也一样:
V_t+rSV_s+0.5sigma^2S^2V_ss=rV, with V(S=100)=1, and V(0)=0.

第二问:
1.如果初始价格S>K,且还假设r=0,那依然还不是non-arbitrage的.因为你可以做任何的
replication portfolio.
如果假设r>0,且股票没有分红的话,那这个portfolio没法造,因为你买股票要借钱,银行
收利息的.万一S用很长很时间才hit K,那你利息就亏大了.

2.这个时候risk neutral的定价就还是是E(exp(-r*tau)),tau是hit K的stopping time
.这个可以通过构造exp(-r*tau+clnS)成为martingale去算.

**至于是不是non-arbitrage的唯一定价..没想清楚呢..好像是..**

3.用PDE的话,带一个boundary(实际上是stopping time的boundary condtion),就可以
用类似wilmott那本书的推理方法去解,那就是V(s)=BS^{-2r/sigma^2}.然后类似思路去
求B.只不过这里的V(S*)=1,instead of V(s*)=E-S* on wilmott's book.

同样的,PDE的来源,本来就是在假设了risk-neutral的measure下面的SDE推到出来的.所
以这个结果应该跟上面的第二种一样,都是risk-neutral的定价.至于是不是non-
arbitrage的唯一定价..没想清楚呢...

1. How to hedge a digital option.
   
2. What are the differences between future and forward, which of these will
   have credit or interest risk.
   
3. Three IID r.v ~uniform(0,1) distribution, what is prob of x1+x2>x3. You
   need to get the result very quickly.
   
4. What is pair trading, how to find two pairs.
   
5. What is virtual function. What is pure virtual function. Why we need
   abstract class?
   
6. Difference between declare and definition? Can we declare abstract class ?
   
7. Monte Carlo method, methods for variance reduction? How to choose best
   parameter for control variate. How to simulate the deep out the money option( Importance sampling)
   
8. What is CDS and IRS. How to price.

Requirements

1. Can you name a number of non-functional (or quality) requirements?
2. What is your advice when a customer wants high performance, high usability and high security?
3. Can you name a number of different techniques for specifying requirements? What works best in which case?
4. What is requirements tracing? What is backward tracing vs. forward tracing?
5. Which tools do you like to use for keeping track of requirements?
6. How do you treat changing requirements? Are they good or bad? Why?
7. How do you search and find requirements? What are possible sources?
8. How do you prioritize requirements? Do you know different techniques?
9. Can you name the responsibilities of the user, the customer and the developer in the requirements process?
10. What do you do with requirements that are incomplete or incomprehensible?

Functional Design

1. What are metaphors used for in functional design? Can you name some successful examples?
2. How can you reduce the user's perception of waiting when some functions take a lot of time?
3. Which controls would you use when a user must select multiple items from a big list, in a minimal amount of space?
4. Can you name different measures to guarantee correctness of data entry?
5. Can you name different techniques for prototyping an application?
6. Can you name examples of how an application can anticipate user behavior?
7. Can you name different ways of designing access to a large and complex list of features?
8. How would you design editing twenty fields for a list of 10 items? And editing 3 fields for a list of 1000 items?
9. What is the problem of using different colors when highlighting pieces of a text?
10. Can you name some limitations of a web environment vs. a Windows environment?

Technical Design

1. What do low coupling and high cohesion mean? What does the principle of encapsulation mean?
2. How do you manage conflicts in a web application when different people are editing the same data?
3. Do you know about design patterns? Which design patterns have you used, and in what situations?
4. Do you know what a stateless business layer is? Where do long-running transactions fit into that picture?
5. What kinds of diagrams have you used in designing parts of an architecture, or a technical design?
6. Can you name the different tiers and responsibilities in an N-tier architecture?
7. Can you name different measures to guarantee correctness and robustness of data in an architecture?
8. Can you name any differences between object-oriented design and component-based design?
9. How would you model user authorization, user profiles and permissions in a database?
10. How would you model the animal kingdom (with species and their behavior) as a class system?

Construction

1. How do you make sure that your code can handle different kinds of error situations?
2. Can you explain what Test-Driven Development is? Can you name some principles of Extreme Programming?
3. What do you care about most when reviewing somebody else's code?
4. When do you use an abstract class and when do you use an interface?
5. Apart from the IDE, which other favorite tools do you use that you think are essential to you?
6. How do you make sure that your code is both safe and fast?
7. When do you use polymorphism and when do you use delegates?
8. When would you use a class with static members and when would you use a Singleton class?
9. Can you name examples of anticipating changing requirements in your code?
10. Can you describe the process you use for writing a piece of code, from requirements to delivery?

Algorithms

1. How do you find out if a number is a power of 2? And how do you know if it is an odd number?
2. How do you find the middle item in a linked list?
3. How would you change the format of all the phone numbers in 10,000 static html web pages?
4. Can you name an example of a recursive solution that you created?
5. Which is faster: finding an item in a hashtable or in a sorted list?
6. What is the last thing you learned about algorithms from a book, magazine or web site?
7. How would you write a function to reverse a string? And can you do that without a temporary string?
8. What type of language do you prefer for writing complex algorithms?
9. In an array with integers between 1 and 1,000,000 one value is in the array twice. How do you determine which one?
10. Do you know about the Traveling Salesman Problem?

Data Structures

1. How would you implement the structure of the London underground in a computer's memory?
2. How would you store the value of a color in a database, as efficiently as possible?
3. What is the difference between a queue and a stack?
4. What is the difference between storing data on the heap vs. on the stack?
5. How would you store a vector in N dimensions in a datatable?
6. What type of language do you prefer for writing complex data structures?
7. What is the number 21 in binary format? And in hex?
8. What is the last thing you learned about data structures from a book, magazine or web site?
9. How would you store the results of a soccer/football competition (with teams and scores) in an XML document?
10. Can you name some different text file formats for storing unicode characters?

Testing

1. Do you know what a regression test is? How do you verify that new changes have not broken existing features?
2. How can you implement unit testing when there are dependencies between a business layer and a data layer?
3. Which tools are essential to you for testing the quality of your code?
4. What types of problems have you encountered most often in your products after deployment?
5. Do you know what code coverage is? What types of code coverage are there?
6. Do you know the difference between functional testing and exploratory testing? How would you test a web site?
7. What is the difference between a test suite, a test case and a test plan? How would you organize testing?
8. What kind of tests would you include for a smoke test of an ecommerce web site?
9. What can you do reduce the chance that a customer finds things that he doesn't like during acceptance testing?
10. Can you tell me something that you have learned about testing and quality assurance in the last year?

Maintenance

1. What kind of tools are important to you for monitoring a product during maintenance?
2. What is important when updating a product that is in production and is being used?
3. How do you find an error in a large file with code that you cannot step through?
4. How can you make sure that changes in code will not affect any other parts of the product?
5. How do you create technical documentation for your products?
6. What measures have you taken to make your software products more easily maintainable?
7. How can you debug a system in a production environment, while it is being used?
8. Do you know what load balancing is? Can you name different types of load balancing?
9. Can you name reasons why maintenance of software is the biggest/most expensive part of an application's life cycle?
10. What is the difference between re-engineering and reverse engineering?

Configuration Management

1. Do you know what a baseline is in configuration management? How do you freeze an important moment in a project?
2. Which items do you normally place under version control?
3. How can you make sure that team members know who changed what in a software project?
4. Do you know the differences between tags and branches? When do you use which?
5. How would you manage changes to technical documentation, like the architecture of a product?
6. Which tools do you need to manage the state of all digital information in a project? Which tools do you like best?
7. How do you deal with changes that a customer wants in a released product?
8. Are there differences in managing versions and releases?
9. What is the difference between managing changes in text files vs. managing changes in binary files?
10. How would you treat simultaneous development of multiple RfC's or increments and maintenance issues?

Project Management

1. How many of the three variables scope, time and cost can be fixed by the customer?
2. Who should make estimates for the effort of a project? Who is allowed to set the deadline?
3. Do you prefer minimization of the number of releases or minimization of the amount of work-in-progress?
4. Which kind of diagrams do you use to track progress in a project?
5. What is the difference between an iteration and an increment?
6. Can you explain the practice of risk management? How should risks be managed?
7. Do you prefer a work breakdown structure or a rolling wave planning?
8. What do you need to be able to determine if a project is on time and within budget?
9. Can you name some differences between DSDM, Prince2 and Scrum?
10. How do you agree on scope and time with the customer, when the customer wants too much?

1. Given a Binary Search Tree, write a program to print the kth smallest element without using any static/global variable. You can’t pass the value k to any function also.
2. What are the 4 basics of OOP?
3. Define Data Abstraction. What is its importance?
4. Given an array of size n. It contains numbers in the range 1 to n. Each number is present at least once except for 2 numbers. Find the missing numbers.
5. Given an array of size n. It contains numbers in the range 1 to n. Find the numbers which aren’t present.
6. Given a string,find the first un-repeated character in it? Give some test cases
7. You are given a dictionary of all valid words. You have the following 3 operations permitted on a word: delete a character, insert a character, replace a character. Now given two words - word1 and word2 - find the minimum number of steps required to convert word1 to word2. (one operation counts as 1 step.)
8. Given a cube of size n*n*n (i.e made up of n^3 smaller cubes), find the number of smaller cubes on the surface. Extend this to k-dimension.
9. What is a C array and illustrate the how is it different from a list.
10. What is the time and space complexities of merge sort and when is it preferred over quick sort?
11. Write a function which takes as parameters one regular expression(only ? and * are the special characters) and a string and returns whether the string matched the regular expression.
12. Given n red balls and m blue balls and some containers, how would you distribute those balls among the containers such that the probability of picking a red ball is maximized, assuming that the user randomly chooses a container and then randomly picks a ball from that.
13. Find the second largest element in an array with minimum no of comparisons and give the minimum no of comparisons needed on an array of size N to do the same.
14. Given an array of size n, containing every element from 1 to n+1, except one. Find the missing element.
15. How do you convert a decimal number to its hexa-decimal equivalent.Give a C code to do the same
16. Explain polymorphism. Provide an example.
17. Given an array all of whose elements are positive numbers, find the maximum sum of a subsequence with the constraint that no 2 numbers in the sequence should be adjacent in the array. So 3 2 7 10 should return 13 (sum of 3 and 10) or 3 2 5 10 7 should return 15 (sum of 3, 5 and 7)
18. You are given some denominations of coins in an array (int denom[])and infinite supply of all of them. Given an amount (int amount), find the minimum number of coins required to get the exact amount. What is the method called?
19. Given an array of size n. It contains numbers in the range 1 to n. Each number is present at least once except for 1 number. Find the missing number.

1. Install MySQL
   
   

   $ apt-get update
   $ apt-get upgrade --show-upgraded
   $ apt-get install mysql-server
   
   You will be prompted to set a password for the MySQL root user.
   Choose a strong password and keep it in a safe place for future 
   reference.
   
   The MySQL server package will be installed on your server, along 
   with dependencies and client libraries. Next, make sure your 
   /etc/hosts file has proper entries, similar to the ones shown below:
   
   $ gedit /etc/hosts

   127.0.0.1    localhost.localdomain    localhost
   12.34.56.78  servername.mydomain.com  servername
   After installing MySQL, it's recommended that you run 
   mysql_secure_installation, a program that helps secure MySQL. 
   mysql_secure_installation gives you the option to disable root 
   logins from outside localhost, remove anonymous user accounts, 
   and the option to remove the test database. Additionally, it 
   allows you to set your root password. Run the following command 
   to execute the program:
   
   mysql_secure_installation
   
   After running mysql_secure_installation, MySQL is secure and 
   ready to be configured.
   
   

2. Configure MySQL
   
   By default, MySQL makes some assumptions about your server environment with respect to memory. To configure MySQL more conservatively, you'll need to edit some settings in the configuration file (/etc/mysql/my.cnf) as follows:
   
   

   
   key_buffer = 16K
   max_allowed_packet = 1M
   thread_stack = 64K
   table_cache = 4
   sort_buffer = 64K
   net_buffer_length = 2K

   
   These settings are only suggested values for a low memory environment; please feel free to tune them to appropriate values for your server. Consult the "More Information" section at the end of this tutorial for additional resources for this topic.
   
   MySQL will bind to localhost (127.0.0.1) by default. Allowing unrestricted access to MySQL on a public IP not advised, but you may change the address it listens on by modifying the bind-address parameter. If you decide to bind MySQL to your public IP, you should implement firewall rules that only allow connections from specific IP addresses.
   
   
3. Using MySQL
   
   The standard tool for interacting with MySQL is the mysql client program. To get started, issue the following command at your prompt:
   
   
   

   mysql -u root -p

   
   You will be prompted to enter the root MySQL user's password. Enter the password you assigned when you installed MySQL, and you'll be presented with the MySQL monitor display:
   
   
   

   Welcome to the MySQL monitor.  Commands end with ; or \g.
   Your MySQL connection id is 41
   Server version: 5.1.37-1ubuntu5 (Ubuntu)
   
   Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
   
   mysql>

   
   If you've forgotten your root password, use the package reconfiguration tool to change that password:
   
   
   

   dpkg-reconfigure mysql-server-5.1

   
   To generate a list of commands for the MySQL prompt type \h:
   
   
   

   List of all MySQL commands:
   Note that all text commands must be first on line and end with ';'
   ?         (\?) Synonym for `help'.
   clear     (\c) Clear command.
   connect   (\r) Reconnect to the server. Optional arguments are db and host.
   delimiter (\d) Set statement delimiter. NOTE: Takes the rest of the line as new delimiter.
   edit      (\e) Edit command with $EDITOR.
   ego       (\G) Send command to mysql server, display result vertically.
   exit      (\q) Exit mysql. Same as quit.
   go        (\g) Send command to mysql server.
   help      (\h) Display this help.
   nopager   (\n) Disable pager, print to stdout.
   notee     (\t) Don't write into outfile.
   pager     (\P) Set PAGER [to_pager]. Print the query results via PAGER.
   print     (\p) Print current command.
   prompt    (\R) Change your mysql prompt.
   quit      (\q) Quit mysql.
   rehash    (\#) Rebuild completion hash.
   source    (\.) Execute an SQL script file. Takes a file name as an argument.
   status    (\s) Get status information from the server.
   system    (\!) Execute a system shell command.
   tee       (\T) Set outfile [to_outfile]. Append everything into given outfile.
   use       (\u) Use another database. Takes database name as argument.
   charset   (\C) Switch to another charset. Might be needed for processing binlog with multi-byte charsets.
   warnings  (\W) Show warnings after every statement.
   nowarning (\w) Don't show warnings after every statement.
   
   For server side help, type 'help contents'
   
   mysql>

   
   Let's create a database and assign a user to it. Issue the following commands at the MySQL prompt:
   
   
   

   CREATE DATABASE testdb;
   
   CREATE USER 'testuser'@localhost IDENTIFIED BY 's8723hk2';
   
   GRANT ALL PRIVILEGES ON testdb.* TO 'testuser'@localhost;
   
   exit

   
   Now let's log back into the MySQL client as testuser and create a sample table called "customers." Issue the following commands:
   
   
   

   mysql -u testuser -p
   
   USE testdb;
   
   CREATE TABLE customers (customer_id INT NOT NULL AUTO_INCREMENT PRIMARY KEY, first_name TEXT, last_name TEXT);

   
   This creates a table with a customer ID field of the type INT for integer (auto-incremented for new records, used as the primary key), as well as two fields for storing the customer's name. Of course, you'd probably want to store much more information than this on a customer, but it's a good example of a common case.

#include <boost/math/distributions/normal.hpp> // for normal_distribution
using boost::math::normal; // typedef provides default type is double.

#include <iostream>
using std::cout; using std::endl; using std::left; using std::showpoint; using std::noshowpoint;

#include <iomanip>
using std::setw; using std::setprecision;

#include <limits>
using std::numeric_limits;

int main()
{
// Generate a normal random number
normal s; // (default mean = zero, and standard deviation = unity)
cout << "Standard normal distribution, mean = "<< s.mean()
<< ", standard deviation = " << s.standard_deviation() << endl;

// Calculate PDF
cout << "Probability distribution function values" << endl;
cout << " z  pdf " << endl;
cout.precision(5);
for (double z = -10; z < 10; z+= 1) 
{
cout << left << setprecision(3) << setw(6) << z << " "
<< setprecision(17) << setw(12) << pdf(s, z) << endl;
}
cout.precision(6); // default


// Calculate CDF
cout << "Integral (area under the curve) from - infinity up to z " << endl;
cout << " z   cdf " << endl;
for (double z = -5; z < 5; z+= 1)
{
cout << left << setprecision(3) << setw(6) << z << " "
<< setprecision(17) << setw(12) << cdf(s, z) << endl;
}
cout.precision(6); // default


// Calculate quantile
cout << "95% of area has a z below " << quantile(s, 0.95) << endl;

return 0;
}

• Download installer binary from Boostpro Computing and install.
  
  
• To build from Visual Studio IDE
  Setting up #include paths in Microsoft Visual Studio
  Right click the project name in the solution explorer > Properties > C/C++ > General > Additional Include Directories, enter the path to the Boost root directory, for example
  C:\Program Files\boost\boost_1_42
  
  In C++ code, include something like
#include <boost/lambda.hpp>


• To link from within Visual Studio IDE
  Right click the project name in the solution explorer > Properties > Linker > General > Additional Library Directories, enter the path to the Boost root directory, for example
  C:\Program Files\boost\boost_1_42\lib\
  
  

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