b***k
发帖数: 2673 | 1 大家讨论一下。
option pricing
1) S = 100, K = 100, r = 0, T = 1, sigma = 0.2. What is the price of
call/put if sigma increases, r increases? If S becomes S = 110, how delta
changes when sigma increases (up to infinity)? Change it to digital option
and answer the question again. He is interested in the
intuition/explanation, NOT the formulas.
2) Cov(W_s^2, W_t^2] = ?, 0<= s <= t
3) Difference between FX option and equity option AND WHY? I answered from
implied vol.
4) I have $10, you have $5, $1 a bid o | l******f
发帖数: 568 | 2 算了一下 2）， 2s^2 ?
【在 b***k 的大作中提到】
: 大家讨论一下。
: option pricing
: 1) S = 100, K = 100, r = 0, T = 1, sigma = 0.2. What is the price of
: call/put if sigma increases, r increases? If S becomes S = 110, how delta
: changes when sigma increases (up to infinity)? Change it to digital option
: and answer the question again. He is interested in the
: intuition/explanation, NOT the formulas.
: 2) Cov(W_s^2, W_t^2] = ?, 0<= s <= t
: 3) Difference between FX option and equity option AND WHY? I answered from
: implied vol.
| s*******r
发帖数: 60 | 3 2) 2S^2
【在 b***k 的大作中提到】
: 大家讨论一下。
: option pricing
: 1) S = 100, K = 100, r = 0, T = 1, sigma = 0.2. What is the price of
: call/put if sigma increases, r increases? If S becomes S = 110, how delta
: changes when sigma increases (up to infinity)? Change it to digital option
: and answer the question again. He is interested in the
: intuition/explanation, NOT the formulas.
: 2) Cov(W_s^2, W_t^2] = ?, 0<= s <= t
: 3) Difference between FX option and equity option AND WHY? I answered from
: implied vol.
| s*******r
发帖数: 60 | 4 3) 2/3 ?
50 ?
unfaired coin, 构造鞅？
【在 b***k 的大作中提到】
: 大家讨论一下。
: option pricing
: 1) S = 100, K = 100, r = 0, T = 1, sigma = 0.2. What is the price of
: call/put if sigma increases, r increases? If S becomes S = 110, how delta
: changes when sigma increases (up to infinity)? Change it to digital option
: and answer the question again. He is interested in the
: intuition/explanation, NOT the formulas.
: 2) Cov(W_s^2, W_t^2] = ?, 0<= s <= t
: 3) Difference between FX option and equity option AND WHY? I answered from
: implied vol.
| l******8
发帖数: 32 | 5 My god, this is my feedback email to HVu last friday.
2) -- Yes 2s^2
4) -- I still don't know how to handle the case of p != 0.5. The interviewer bought my Markov chain approach reluctantly so I believe that he has an easier way in hand. Another way I can imagine is exponential martingale,not sure if it is simpler though. | b***k
发帖数: 2673 | 6 all right, my rudness. I admit I got these questions from a coworker of HVu.
but...
why do you share your interview questions with HH instead of sharing here?
be afraid of ppl stealing your experience?
;-)
interviewer bought my Markov chain approach reluctantly so I believe that he
has an easier way in hand. Another way I can imagine is exponential
martingale,not sure if it is simpler tho
【在 l******8 的大作中提到】
: My god, this is my feedback email to HVu last friday.
: 2) -- Yes 2s^2
: 4) -- I still don't know how to handle the case of p != 0.5. The interviewer bought my Markov chain approach reluctantly so I believe that he has an easier way in hand. Another way I can imagine is exponential martingale,not sure if it is simpler though.
| j*****4
发帖数: 292 | 7 Q4 is the famous gambler's ruin problem. (formally, it's a (biased)random wa
lk with absorbing states)
As is stated in XF Zhou's book, it is widely used in quant interviews.
I think anyone who wants to try quant jobs should know clearly the solutions
and the math behind.
Here I give some summary of solutions I know. Typically three methods can be
used to solve this problem:
1).
Reccusion method
P96, Ross, A first course in probability, 7ed
or P83, Xinfeng Zhou's book.
2).
Markov chain method.
P1
【在 l******8 的大作中提到】
: My god, this is my feedback email to HVu last friday.
: 2) -- Yes 2s^2
: 4) -- I still don't know how to handle the case of p != 0.5. The interviewer bought my Markov chain approach reluctantly so I believe that he has an easier way in hand. Another way I can imagine is exponential martingale,not sure if it is simpler though.
| l******8
发帖数: 32 | 8 Be careful, you won't get it if I don't share. Why do you think I wrote it?
But thank for posting it here and save me some time.
HVu.
he
【在 b***k 的大作中提到】
: all right, my rudness. I admit I got these questions from a coworker of HVu.
: but...
: why do you share your interview questions with HH instead of sharing here?
: be afraid of ppl stealing your experience?
: ;-)
:
: interviewer bought my Markov chain approach reluctantly so I believe that he
: has an easier way in hand. Another way I can imagine is exponential
: martingale,not sure if it is simpler tho
| c***z
发帖数: 6348 | 9 God, I have NO idea about any of these! Oh, wait, maybe except #4.
I can only count on my luck it seems.
【在 b***k 的大作中提到】
: 大家讨论一下。
: option pricing
: 1) S = 100, K = 100, r = 0, T = 1, sigma = 0.2. What is the price of
: call/put if sigma increases, r increases? If S becomes S = 110, how delta
: changes when sigma increases (up to infinity)? Change it to digital option
: and answer the question again. He is interested in the
: intuition/explanation, NOT the formulas.
: 2) Cov(W_s^2, W_t^2] = ?, 0<= s <= t
: 3) Difference between FX option and equity option AND WHY? I answered from
: implied vol.
| c***z
发帖数: 6348 | 10 What is HVu? Google gives nothing meaningful...
Thanks for sharing! | | | I****k
发帖数: 35 | 11 可以给个详细的推导么？
我算出来的是2s^2 + st
【在 s*******r 的大作中提到】
: 2) 2S^2
| s********7
发帖数: 52 | 12 to price FX option you need interest rate of 2 currencies and no dividend.
that's the major difference from equity options | i*****e
发帖数: 159 | 13 怎么算E[Ws^4] 或者是Var[Ws^2]?
interviewer bought my Markov chain approach reluctantly so I believe that he
has an easier way in hand. Another way I can imagine is exponential
martingale,not sure if it is simpler though.
【在 l******8 的大作中提到】
: My god, this is my feedback email to HVu last friday.
: 2) -- Yes 2s^2
: 4) -- I still don't know how to handle the case of p != 0.5. The interviewer bought my Markov chain approach reluctantly so I believe that he has an easier way in hand. Another way I can imagine is exponential martingale,not sure if it is simpler though.
| j*****4
发帖数: 292 | 14 W_s^4=\int_0^s dW_t^4,then use Ito's formula
he
【在 i*****e 的大作中提到】
: 怎么算E[Ws^4] 或者是Var[Ws^2]?
:
: interviewer bought my Markov chain approach reluctantly so I believe that he
: has an easier way in hand. Another way I can imagine is exponential
: martingale,not sure if it is simpler though.
| i*****e
发帖数: 159 | 15 thanks
【在 j*****4 的大作中提到】
: W_s^4=\int_0^s dW_t^4,then use Ito's formula
:
: he
| m*****n
发帖数: 2152 | 16 然后还是不会， dW_t4^4 = 6W_t^2 dt + 4W_t^3 dW_t 对不对？然后怎么办？
OK，我知道了，是不是这样
E(W_s^4)=E(\int_0^W_s dW_t^4)=\int_0^s E(6W_t^2) dt + 4 \int_0^s E(W_t^3)
dW_t
E(W_t^3) = 0, E(6W_t^2) = 6t
So E(W_s^4) = \int_0^s 6t dt = 3s^2
如果是这样的话，要不要证明 E 和 \int 是可以commute的啊？
【在 j*****4 的大作中提到】
: W_s^4=\int_0^s dW_t^4,then use Ito's formula
:
: he
| j*****4
发帖数: 292 | 17 Ito Integral Process has zero expectation, thus,E(int_0^r W_t^3dW_t)=0
【在 m*****n 的大作中提到】
: 然后还是不会， dW_t4^4 = 6W_t^2 dt + 4W_t^3 dW_t 对不对？然后怎么办？
: OK，我知道了，是不是这样
: E(W_s^4)=E(\int_0^W_s dW_t^4)=\int_0^s E(6W_t^2) dt + 4 \int_0^s E(W_t^3)
: dW_t
: E(W_t^3) = 0, E(6W_t^2) = 6t
: So E(W_s^4) = \int_0^s 6t dt = 3s^2
: 如果是这样的话，要不要证明 E 和 \int 是可以commute的啊？
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