c****o
发帖数: 1280 | 1 I will not disclose the name of the companys
1.Play a game. I am giving you $1, and the price of per share have mean $1,
variance 5 cents, how many share do I expected to get?(Hint: variance is
small quantity, use taylor expansion to 1/(1+x))
2.How to replicate binary option from call option, given the option prices
for ALL strike price, what is the value of the binary?
3.From 2, if the option pays a delta function, namely, pay 1 when s is
within epsilon neighborhood of K, price this option?
4.For Arbitrary payoff, what is the price given 3.
5.Prove that binomial distribution approach possion distribution?(wiki
possion distribution)
6. What is the precision for "double" in c++?(1e-15) Given CFD of normal
distribution, estimate x such that N(x)=1 is stored as double.(I got 32, the
interviewer said they can get 8....)
7.Give me a stable scheme to solve heat equation. Unconditionally stable or
conditionally?Explicite?
8.Stock today 100, tomorrow 110,100,0,price ATM call option.
(Incomplete market) Give bound of the price then
9. Consider the foreign exchange model ds=(r-Q)sdt+sigma sdw(t), what does r
and Q stands for? Consider u=1/s, calculate du.explain the paradox(Change
of numeria, shreve book has a very nice explainition)
10. x martingale? sin(x) martingale ot not?
11.derive the BS PDE. If stock follows ds=adt+bdw(t), what is the new PDE?
12.explian why volitility increse, the vanilla option price increase.What is
the price when sigma=0,infinity. Will the result be same if it is a binary
option?
13.what is the price of option if pay max(s(s-k),0)?(change of numeria)
14.3 coin, 2 fair,one double headed,flip a coin, get 3 heads in a row? what
is the probability of getting 4 heads in a row?
15.monte carlo reduction methods? For control variable method,if the
corralation if 0.8, how much can be reduced
16.3 option,k=95,100,105, price=7,5,2, any arbitrage opportunity?
17.If Interest rate follows BM, price a zero coupon bond pays $1 at T,
is the assumption reasonable?
18.x,y~N(0,1), independent, what is E(x|x+y=1), what about variance
19A zero coupon bond, pays $100 face value, current $95, a contract pays $1
when the bond hits $98, price the contract.
20.explain forward rate agreement? Under forward measure, it is a martingale
? what about Risk neutral measure.
These are all from phone interviews from different companies, I skip some
standard questions that appear in the green book, I will post more from my
onsite tomorrow.
Good luck to everybody! | w******i
发帖数: 503 | 2 Thanks and congratulations, LZ. great post.
will not disclose the name of the companys
1.Play a game. I am giving you $1, and the price of per share have mean $1,
variance 5 cents, how many share do I expected to get?(Hint: variance is
small quantity, use taylor expansion to 1/(1+x))
2.How to replicate binary option from call option, given the option prices
for ALL strike price, what is the value of the binary?
3.From 2, if the option pays a delta function, namely, pay 1 when s is
within epsilon neighborhood of K, price this option?
4.For Arbitrary payoff, what is the price given 3.
5.Prove that binomial distribution approach possion distribution?(wiki
possion distribution)
6. What is the precision for "double" in c++?(1e-15) Given CFD of normal
distribution, estimate x such that N(x)=1 is stored as double.(I got 32, the
interviewer said they can get 8....)
7.Give me a stable scheme to solve heat equation. Unconditionally stable or
conditionally?Explicite?
8.Stock today 100, tomorrow 110,100,0,price ATM call option.
(Incomplete market) Give bound of the price then
9. Consider the foreign exchange model ds=(r-Q)sdt+sigma sdw(t), what does r
and Q stands for? Consider u=1/s, calculate du.explain the paradox(Change
of numeria, shreve book has a very nice explainition)
10. x martingale? sin(x) martingale ot not?
11.derive the BS PDE. If stock follows ds=adt+bdw(t), what is the new PDE?
12.explian why volitility increse, the vanilla option price increase.What is
the price when sigma=0,infinity. Will the result be same if it is a binary
option?
13.what is the price of option if pay max(s(s-k),0)?(change of numeria)
14.3 coin, 2 fair,one double headed,flip a coin, get 3 heads in a row? what
is the probability of getting 4 heads in a row?
15.monte carlo reduction methods? For control variable method,if the
corralation if 0.8, how much can be reduced
16.3 option,k=95,100,105, price=7,5,2, any arbitrage opportunity?
17.If Interest rate follows BM, price a zero coupon bond pays $1 at T,
is the assumption reasonable?
18.x,y~N(0,1), independent, what is E(x|x+y=1), what about variance
19A zero coupon bond, pays $100 face value, current $95, a contract pays $1
when the bond hits $98, price the contract.
20.explain forward rate agreement? Under forward measure, it is a martingale
? what about Risk neutral measure.
These are all from phone interviews from different companies, I skip some
standard questions that appear in the green book, I will post more from my
onsite tomorrow.
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| w*****m
发帖数: 414 | | t*******y
发帖数: 637 | 4 congrats and thx for sharing!
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| i****k
发帖数: 39 | | l****e
发帖数: 1718 | 6 cong, would you mind sharing your background? | c****o
发帖数: 1280 | 7 Ivy League
math Ph.D
【在 l****e 的大作中提到】
: cong, would you mind sharing your background?
| B******5
发帖数: 4676 | 8 Cong to you and your LD's offers | l*********t
发帖数: 89 | 9 Great post! Thanks a lot~ | d**********9
发帖数: 5215 | 10 strong background, cong
【在 c****o 的大作中提到】
: Ivy League
: math Ph.D
| | | d*j
发帖数: 13780 | | w**********y
发帖数: 1691 | | J**********g
发帖数: 213 | 13 congs and enjoy your weekend now... | a*****r
发帖数: 681 | 14 lg or lp or both got the offers? | c****o
发帖数: 1280 | 15 we use the same id
【在 a*****r 的大作中提到】
: lg or lp or both got the offers?
| A*******u
发帖数: 66 | 16 Cong! Super Cow~~
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| w*****e
发帖数: 158 | | j********t
发帖数: 97 | 18 Congratulations!
What's answer to question 1? Thanks.
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| s***o
发帖数: 60 | 19 3ks for sharing and cong on your offers. have a nice weekend:) | c****o
发帖数: 1280 | 20 版主给点包子呗。。。。。都发光了。。。。。。。。。穷的叮当响了
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| | | o*******6
发帖数: 6113 | | c****o
发帖数: 1280 | 22 They do give hints if you got stuck
【在 o*******6 的大作中提到】
: 这些问题想在电话上回答清楚还挺有难度的啊
| k*******d
发帖数: 1340 | | n****e
发帖数: 629 | 24 呃…………我们组昨天刚发了个offer.......
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| d*j
发帖数: 13780 | 25 原来是你们组啊
大牛集中营。。。。
【在 n****e 的大作中提到】
: 呃…………我们组昨天刚发了个offer.......
:
: 1,
| u********e
发帖数: 263 | 26 那让此新人请个客庆祝庆祝吧
【在 n****e 的大作中提到】
: 呃…………我们组昨天刚发了个offer.......
:
: 1,
| d*j
发帖数: 13780 | 27 能叫上我吗？
【在 u********e 的大作中提到】
: 那让此新人请个客庆祝庆祝吧
| u********e
发帖数: 263 | 28 让情圣也叫上我！
【在 d*j 的大作中提到】
: 能叫上我吗？
| d*j
发帖数: 13780 | 29 然后你在叫上我
【在 u********e 的大作中提到】
: 让情圣也叫上我！
| n****e
发帖数: 629 | 30 你们统统去死吧
【在 u********e 的大作中提到】
: 让情圣也叫上我！
| | | s*******s
发帖数: 1568 | 31 有饭吃，这种好事不叫我？wow
【在 n****e 的大作中提到】
: 你们统统去死吧
| d*j
发帖数: 13780 | 32 都叫上， 我们用面试题那个 trick
看看平均工资是多少吧？
【在 s*******s 的大作中提到】
: 有饭吃，这种好事不叫我？wow
| s*******s
发帖数: 1568 | 33 大牛你是outlier，说不定最后以为算错了
【在 d*j 的大作中提到】
: 都叫上， 我们用面试题那个 trick
: 看看平均工资是多少吧？
| d*j
发帖数: 13780 | 34 嗯， 太低了。。。 拖累了大家
哭死了
【在 s*******s 的大作中提到】
: 大牛你是outlier，说不定最后以为算错了
| c****o
发帖数: 1280 | 35 大牛，以后就在你手下干活了，多多关照啊
【在 n****e 的大作中提到】
: 呃…………我们组昨天刚发了个offer.......
:
: 1,
| s*******s
发帖数: 1568 | 36 看来招10人有8个是中国人
【在 c****o 的大作中提到】
: 大牛，以后就在你手下干活了，多多关照啊
| H******i
发帖数: 4704 | 37 我一个问题也不会, 我给你100个伪币你把答案告诉我, 好吗? | n****e
发帖数: 629 | 38 嗯 最近招的全是中国人
我之前中国人比例是0%
现在稳步上升到50%
【在 s*******s 的大作中提到】
: 看来招10人有8个是中国人
| d*j
发帖数: 13780 | 39 。。。。。。
当时面试我的有三个同胞啊 。。。
不过可能不是一个组的， 你们有两个组吧
【在 n****e 的大作中提到】
: 嗯 最近招的全是中国人
: 我之前中国人比例是0%
: 现在稳步上升到50%
| n****e
发帖数: 629 | 40 嗯 现在有两个组了 不过隔壁组也就俩中国人啊
估计是拉了几个走廊那边的来面您
隔壁组的老大眼界高 喜欢招imo金牌之类的 怪不得会找上您啊
【在 d*j 的大作中提到】
: 。。。。。。
: 当时面试我的有三个同胞啊 。。。
: 不过可能不是一个组的， 你们有两个组吧
| | | u********e
发帖数: 263 | 41 反正现在到处都是同胞，我就听到几砣trader叫我们chinatown...
【在 d*j 的大作中提到】
: 。。。。。。
: 当时面试我的有三个同胞啊 。。。
: 不过可能不是一个组的， 你们有两个组吧
| s*******s
发帖数: 1568 | 42 赞阿
我上次是听说你们组招人目前80％是中国人。。。
【在 n****e 的大作中提到】
: 嗯 最近招的全是中国人
: 我之前中国人比例是0%
: 现在稳步上升到50%
| n****e
发帖数: 629 | 43 那是因为我们这波phd纷纷毕业了。。。
【在 u********e 的大作中提到】
: 反正现在到处都是同胞，我就听到几砣trader叫我们chinatown...
| u********e
发帖数: 263 | 44 你还是赶紧撺掇你们新人请客吧！不请白不请，dream offer一生也没几次！
【在 n****e 的大作中提到】
: 那是因为我们这波phd纷纷毕业了。。。
| d*j
发帖数: 13780 | 45 Mr. Luo ？
所以他没有要我啊， 我太烂了 。。。。
当时面试我的其他两个人都坐在他办公室附近的 desk
【在 n****e 的大作中提到】
: 嗯 现在有两个组了 不过隔壁组也就俩中国人啊
: 估计是拉了几个走廊那边的来面您
: 隔壁组的老大眼界高 喜欢招imo金牌之类的 怪不得会找上您啊
| d*j
发帖数: 13780 | 46 嗯， 重点啊
你还是赶紧撺掇你们新人请客吧！不请白不请，dream offer一生也没几次！
【在 u********e 的大作中提到】
: 你还是赶紧撺掇你们新人请客吧！不请白不请，dream offer一生也没几次！
| f*******y
发帖数: 988 | 47 你们应该出个新面试题，如何在这个trick里面准确知道别人的工资而不暴露自己的真
实工资
【在 s*******s 的大作中提到】
: 大牛你是outlier，说不定最后以为算错了
| f*******y
发帖数: 988 | 48 金牌兄呀
别说金牌了，我这被都没见过有牌子的活人
【在 d*j 的大作中提到】
: Mr. Luo ？
: 所以他没有要我啊， 我太烂了 。。。。
: 当时面试我的其他两个人都坐在他办公室附近的 desk
| w**********y
发帖数: 1691 | 49 wow.崇拜崇拜!简直就像见了活佛一样!!daj你是我的偶像..估计金牌神医花街大牛,你
算世界头一号!
【在 f*******y 的大作中提到】
: 金牌兄呀
: 别说金牌了，我这被都没见过有牌子的活人
| d*j
发帖数: 13780 | 50 。。。。。。。。。
你没看出来他在骂人吗？
他的意思是 有了牌子的都是死人了
哈哈
还好我没有
【在 w**********y 的大作中提到】
: wow.崇拜崇拜!简直就像见了活佛一样!!daj你是我的偶像..估计金牌神医花街大牛,你
: 算世界头一号!
| | | g*****5
发帖数: 3285 | 51 hoho.恭喜恭喜。前几天你给我电话啥事？看见帖子才想起来这个问题。
还以为去信奥尔良开会能碰见你呢。
发包子吧。 | s***e
发帖数: 267 | 52 Congratulations!
Sounds like a group in GS?
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| a***u
发帖数: 67 | 53 呼唤后续题目
也呼唤答案！！
3，4，19怎么做的 | P*****s
发帖数: 758 | | a***n
发帖数: 423 | | L*****k
发帖数: 327 | 56 Great, thanks!!!
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| p******e
发帖数: 756 | 57 能说下13题怎么做么。或者有同学有思路么？
13.what is the price of option if pay max(s(s-k),0)?(change of numeria)
thx
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| k*******d
发帖数: 1340 | 58 My idea
用S(t)做numeraire，要算的是在新的measure下的E[max(s(T),K)]，
Let W'(t) be the BM under the new measure, Note that W'(t) = -sigma
*t+W(t), where W(t) is the BM under the original measure, therefore, the
s(t) process under the new measure will be dS(t)/S(t) = (r+sigma^2)t +
sima*W'(t), so the answer is the BM pricing formula with r replaced by
r+sigma^2, with some modifications
【在 p******e 的大作中提到】
: 能说下13题怎么做么。或者有同学有思路么？
: 13.what is the price of option if pay max(s(s-k),0)?(change of numeria)
: thx
:
: 1,
| T*****w
发帖数: 802 | 59 你找到工作了， 你那头像能不能给我用了。。。。。！
【在 c****o 的大作中提到】
: 版主给点包子呗。。。。。都发光了。。。。。。。。。穷的叮当响了
:
: 1,
| p******e
发帖数: 756 | 60 你的w'(t)为什么要定义成\-sigma dt+dw_t?而且好像你的新的measure也不是equivale
nt martingale measure，value也就不一定是
E[max(S(T)-K,0)]了吧
我对change of numeraire的理解是在new numeraire下
\tilde{S(t)}是martingale或者没有dt项。但这里如果把S(t)本身当成new numeraire，
那\tilde{S(t)}=1
理解的不深刻，望大牛们指点
thx
【在 k*******d 的大作中提到】
: My idea
: 用S(t)做numeraire，要算的是在新的measure下的E[max(s(T),K)]，
: Let W'(t) be the BM under the new measure, Note that W'(t) = -sigma
: *t+W(t), where W(t) is the BM under the original measure, therefore, the
: s(t) process under the new measure will be dS(t)/S(t) = (r+sigma^2)t +
: sima*W'(t), so the answer is the BM pricing formula with r replaced by
: r+sigma^2, with some modifications
| | | s****y
发帖数: 12 | 61 终于可以发贴了。。
恭喜楼主！
感谢分享 大赞！ | a********e
发帖数: 508 | 62 超赞！
看了一下，第15题有点疑问。这个问题是不是条件不够充分？
至少要说control variable跟原来的variable的variance一样吧
15.monte carlo reduction methods? For control variable method,if the
corralation if 0.8, how much can be reduced
1,
【在 c****o 的大作中提到】
: I will not disclose the name of the companys
: 1.Play a game. I am giving you $1, and the price of per share have mean $1,
: variance 5 cents, how many share do I expected to get?(Hint: variance is
: small quantity, use taylor expansion to 1/(1+x))
: 2.How to replicate binary option from call option, given the option prices
: for ALL strike price, what is the value of the binary?
: 3.From 2, if the option pays a delta function, namely, pay 1 when s is
: within epsilon neighborhood of K, price this option?
: 4.For Arbitrary payoff, what is the price given 3.
: 5.Prove that binomial distribution approach possion distribution?(wiki
| k****e
发帖数: 647 | 63 不需要。
VR以后，variance = (1-rho^2) Var X，如果我没算错的话
【在 a********e 的大作中提到】
: 超赞！
: 看了一下，第15题有点疑问。这个问题是不是条件不够充分？
: 至少要说control variable跟原来的variable的variance一样吧
: 15.monte carlo reduction methods? For control variable method,if the
: corralation if 0.8, how much can be reduced
:
: 1,
| a********e
发帖数: 508 | 64 嗯，谢谢！
我是看了绿皮书上关于control variate的介绍，那上面讲得比较简单
刚刚wiki了一下明白了，你是对的
【在 k****e 的大作中提到】
: 不需要。
: VR以后，variance = (1-rho^2) Var X，如果我没算错的话
| k****e
发帖数: 647 | 65 客气！
这个问题想想也挺有意思，和control variable的variance无关，挺好的；
可能还有点点implication, literature什么的
【在 a********e 的大作中提到】
: 嗯，谢谢！
: 我是看了绿皮书上关于control variate的介绍，那上面讲得比较简单
: 刚刚wiki了一下明白了，你是对的
| a********e
发帖数: 508 | 66 嗯，仔细想想，这个方法implement起来是要用data估计sample variance/covariacne
其实就是做一个regression, m* = a + b(t-Et), a就是adjusted sample mean
【在 k****e 的大作中提到】
: 客气！
: 这个问题想想也挺有意思，和control variable的variance无关，挺好的；
: 可能还有点点implication, literature什么的
|
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