由买买提看人间百态

boards

本页内容为未名空间相应帖子的节选和存档,一周内的贴子最多显示50字,超过一周显示500字 访问原贴
Quant版 - GS phone interview questions 要包子了!
相关主题
关于希腊字母theta,急,在线等![合集] 发点面经
Some interview questions (zz from Wilmott)[合集] 请推荐 PDE的书
问题:why is it never optimal to early exercise the call when it is equivalent to a put?[合集] 找到工作的总结下好的/差的recruiter吧
Credit Suisse GMAG Quant Summer Institute intern in London, 各位给点建议吧[合集] A quant's day of life (ZZ)
a question about gamma neutral and vega neutral[合集] 请问这里有没有考CQF的
interview questions from GS推荐一个买书的deal
[合集] 请问可以同时找几个Recruiter吗?有个问题始终查找不到相关文献,望有人告知
A quant's day of life (ZZ)非纽约地区的quant职位怎么找?
相关话题的讨论汇总
话题: gamma话题: option话题: became话题: early话题: interest
进入Quant版参与讨论
1 (共1页)
A*****8
发帖数: 73
1
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 bes
d*j
发帖数: 13780
2
恩。。。。。。
a young and tall guy in GS IBD quant group ?

best
.

【在 A*****8 的大作中提到】
: 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 bes

i*****r
发帖数: 1302
3
靠,这种题目要多久回答出来啊,电话里面傻在那怎么办
J******d
发帖数: 506
4
第三题a是不是应该在[0.1)?

best
option,
became
30.

【在 A*****8 的大作中提到】
: 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 bes

A*****8
发帖数: 73
5
Yes, For third question, a between [0,1].
Interviewer give some hint how to solve it if you have difficulty.
w******a
发帖数: 782
6
re
i*****r
发帖数: 1302
7
还是不给好,给了答不出更丢脸

【在 A*****8 的大作中提到】
: Yes, For third question, a between [0,1].
: Interviewer give some hint how to solve it if you have difficulty.

b**********5
发帖数: 51
8
1) for put, raising of interest rate can increase the possibility of early
excises, and for call, it doesn't affect the possibility. But why?
5) Gamma increases.
Are my answers to 1) and 5) right? And could anyone give me your thinking of
the two?
Any comments on other questions?
k*******d
发帖数: 1340
9
第三题那个积分可能是用分部积分法?因为它的形式有些像 x^2 exp(x),而这种形式
常用分部积分法
第四题是 \int_0^t sigma(t)^2 dt吧
为什么interest rate会影响American call的early exercise呢? American Call不是
都不会被early exercise吗?
c*******g
发帖数: 771
10
Re
相关主题
interview questions from GS[合集] 发点面经
[合集] 请问可以同时找几个Recruiter吗?[合集] 请推荐 PDE的书
A quant's day of life (ZZ)[合集] 找到工作的总结下好的/差的recruiter吧
进入Quant版参与讨论
A*****8
发帖数: 73
11
Answer for 5: The Gamma with stock price is like a Delta function. When
volatility increase, this delta function became fatter, so the variance of
Gamma will dependent on the stock price. If at the money, Gamma decrease, if
deep in the money, Gamma increase.
Answer for 3: First sum of a^N, then take first derivative of Sum, then
second derivative.
kitflied, how do you reach the result for question 4?
d*j
发帖数: 13780
12
Ito Isometry

if

【在 A*****8 的大作中提到】
: Answer for 5: The Gamma with stock price is like a Delta function. When
: volatility increase, this delta function became fatter, so the variance of
: Gamma will dependent on the stock price. If at the money, Gamma decrease, if
: deep in the money, Gamma increase.
: Answer for 3: First sum of a^N, then take first derivative of Sum, then
: second derivative.
: kitflied, how do you reach the result for question 4?

k*******d
发帖数: 1340
13
daj大牛能不能讲解一下第一题啊
u******d
发帖数: 770
14
re
d*j
发帖数: 13780
15
哦, 当时高盛的那个小伙子告诉我答案是
从 forward price 考虑
足够了

【在 k*******d 的大作中提到】
: daj大牛能不能讲解一下第一题啊
a**n
发帖数: 3801
16
没影响
american call不发dividend的话和european call一样
都不回去exercise的

【在 k*******d 的大作中提到】
: daj大牛能不能讲解一下第一题啊
O********9
发帖数: 59
17
第三题有个比较接单的解法:
注意到 N^2 a^N 是 Gamma 分布的核。由Gamma分布定义,对任意正实数k 和 b
int_0^{\infty} N^{k-1} e^{- N/b} dN = b^k Gamma(k)
因为
N^2 a^N = N^(3-1) e^{- N ln(1/a)}
所以,
int_0^{\infty} N^2 a^N dN = (1/ln(1/a))^3 Gamma(3) = 2 (1/ln(1/a))^3。
(这里 Gamma(k)=(k-1)!)

best
option,
became
got 30.
price?

【在 A*****8 的大作中提到】
: 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 bes

i*****r
发帖数: 1302
18
不是不发divident都不会early excise的么

【在 d*j 的大作中提到】
: 哦, 当时高盛的那个小伙子告诉我答案是
: 从 forward price 考虑
: 足够了

c*****y
发帖数: 4
19
May I ask where do you take take this interview?
US?

best
.

【在 A*****8 的大作中提到】
: 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 bes

t*******g
发帖数: 373
20
ft, 第三题是我当年的高考题。。。。。。
答案是a(a+1)/(1-a)^3,两次列项求和。

best
.

【在 A*****8 的大作中提到】
: 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 bes

相关主题
[合集] A quant's day of life (ZZ)有个问题始终查找不到相关文献,望有人告知
[合集] 请问这里有没有考CQF的非纽约地区的quant职位怎么找?
推荐一个买书的deal[合集] David Li,Thomas Ho and Sang-Bin Lee?
进入Quant版参与讨论
o******e
发帖数: 74
21
大牛给讲解一下第二题呗?
i**w
发帖数: 71
22

for call option, early exercise means paying the strike price earlier, in
which case you lose the interest earned if by holding the cash longer.
for higher interest rate, you lose more comparing to a lower rate. If the
gain (possible dividend) doesn't cover the loss in interest, one might not
early exercise at all.
so higher interest rate lowers the possibility of early exercise.
special case: if underlying asset doesn't pay dividend, it should never be early exercised. thus interest rate doesn

【在 A*****8 的大作中提到】
: 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 bes

i**w
发帖数: 71
23

best
.
\sum{a^(xN)} = 1/(1-a^x) for 0 then take derivatives on both sides twice
set x=1 in the end
高中时候的解法忘了...

【在 A*****8 的大作中提到】
: 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 bes

i**w
发帖数: 71
24

if
I have no intuition regarding this issue. mind elaborate?
From the expression of Gamma of BS
exp(-delta*t)*N'(d1)

【在 A*****8 的大作中提到】
: Answer for 5: The Gamma with stock price is like a Delta function. When
: volatility increase, this delta function became fatter, so the variance of
: Gamma will dependent on the stock price. If at the money, Gamma decrease, if
: deep in the money, Gamma increase.
: Answer for 3: First sum of a^N, then take first derivative of Sum, then
: second derivative.
: kitflied, how do you reach the result for question 4?

c**********s
发帖数: 295
25
1) assuming we are talking about option on a stock with no devident
call, no early exercise
put, when you exercise early, you loss option value but gain time value. the
higher the interest rate, the higher the time value (and lower option value
), so you have more proba of early exercise.
c**********s
发帖数: 295
26
2) the bound of this option is [4,7]. the higher the correl, the lower this
option.
c**********s
发帖数: 295
27
3) 4) already given before
5) gamma is d^2C / ds^2, which is the underlying risk neutral density. when
vol goes up, ATM gamma does down and out of money gamma goes up.
c**********s
发帖数: 295
28
oh for 2) to get a functional form you can assume both stocks follow gmb and
calculate the joint density with rho and do an integration.
B******5
发帖数: 4676
29
展开说说?
我的答案和Odysseus09的一样。。。

【在 t*******g 的大作中提到】
: ft, 第三题是我当年的高考题。。。。。。
: 答案是a(a+1)/(1-a)^3,两次列项求和。
:
: best
: .

t***j
发帖数: 28
30
"If at the money, Gamma decrease, if deep in the money, Gamma increase. "
We know that the Gamma for call and put are the same. By saying in/out-of-
the-money, what do you mean?

if

【在 A*****8 的大作中提到】
: Answer for 5: The Gamma with stock price is like a Delta function. When
: volatility increase, this delta function became fatter, so the variance of
: Gamma will dependent on the stock price. If at the money, Gamma decrease, if
: deep in the money, Gamma increase.
: Answer for 3: First sum of a^N, then take first derivative of Sum, then
: second derivative.
: kitflied, how do you reach the result for question 4?

相关主题
转贴 This is No Longer Funny By : Paul WilmottSome interview questions (zz from Wilmott)
大家觉得Paul Wilmott的Quantitative Finance值得买么?问题:why is it never optimal to early exercise the call when it is equivalent to a put?
关于希腊字母theta,急,在线等!Credit Suisse GMAG Quant Summer Institute intern in London, 各位给点建议吧
进入Quant版参与讨论
p*****k
发帖数: 318
b******e
发帖数: 118
32
Based on the post on Wilmott, for question 3
sum(n*a^n,n=0..+infinity) = a/(1-a)^2
How to get this?

【在 B******5 的大作中提到】
: 展开说说?
: 我的答案和Odysseus09的一样。。。

S*********g
发帖数: 5298
33
n a^n = a d(a^n)/da

【在 b******e 的大作中提到】
: Based on the post on Wilmott, for question 3
: sum(n*a^n,n=0..+infinity) = a/(1-a)^2
: How to get this?

b******e
发帖数: 118
34
Could you please do one step further? Thx.

【在 S*********g 的大作中提到】
: n a^n = a d(a^n)/da
B******5
发帖数: 4676
35
嗯,理解问题之所在了。。。
他的答案是对的。。。

【在 b******e 的大作中提到】
: Based on the post on Wilmott, for question 3
: sum(n*a^n,n=0..+infinity) = a/(1-a)^2
: How to get this?

S*********g
发帖数: 5298
36
交换求和和求导的顺序
先求和,再求导

【在 b******e 的大作中提到】
: Could you please do one step further? Thx.
1 (共1页)
进入Quant版参与讨论
相关主题
非纽约地区的quant职位怎么找?a question about gamma neutral and vega neutral
[合集] David Li,Thomas Ho and Sang-Bin Lee?interview questions from GS
转贴 This is No Longer Funny By : Paul Wilmott[合集] 请问可以同时找几个Recruiter吗?
大家觉得Paul Wilmott的Quantitative Finance值得买么?A quant's day of life (ZZ)
关于希腊字母theta,急,在线等![合集] 发点面经
Some interview questions (zz from Wilmott)[合集] 请推荐 PDE的书
问题:why is it never optimal to early exercise the call when it is equivalent to a put?[合集] 找到工作的总结下好的/差的recruiter吧
Credit Suisse GMAG Quant Summer Institute intern in London, 各位给点建议吧[合集] A quant's day of life (ZZ)
相关话题的讨论汇总
话题: gamma话题: option话题: became话题: early话题: interest