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 | | 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 | | | | 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 | | u******d
发帖数: 770 | | 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
| | | o******e
发帖数: 74 | | 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?
| | | 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.
|
|
