j********t
发帖数: 97 | 1 1. Calculate \int_{-\infty}^{\infty} \int_{x}^{\infty} xe^{y^3} dydx
2. Repeatedly throw a dice until two even numbers occur in a row or number
is 3 or 5. What's probability of
stopping by two consecutive numbers before 3 or 5?
3. Stock price is 100, strike is 100, maturity is 1 year. Current call price
is 10. Assume you can buy/sell put or
call, borrow/lend cash, purchase stock. But you can't sell stock!!. Please
give tight bound of put option with
the same strike and maturity.
4. Currently stock price X(0) = 100. Maturity is 1 year.
Option 1: Pay $2 if X(1) >= 90.
Option 2: Pay $1 if X(t) >= 90, for any 0 < t < 1
Which option is more valuable and explain reason?
5. X_t and Y_t follow exponential Brownian motion.
dX_t = u_X X_t dt + \sigma_X X_t d U_t
dY_t = u_Y Y_t dt + \sigma_Y Y_t d V_t
where U_t, V_t are standard Brownian motion with correlation coefficient \rho.
Z_t = X_t \ Y_t is exponential Brownian motion. What's drift and volatility
of Z_t?
请大牛们解答，谢谢！ |
k*******d
发帖数: 1340 | 2 2不会做，请大牛解答。。。
3没怎么明白，如果不能sell stock, 那put option拿了干啥？ |
d*j
发帖数: 13780 | 3 CS 的考试？
price
【在 j********t 的大作中提到】
: 1. Calculate \int_{-\infty}^{\infty} \int_{x}^{\infty} xe^{y^3} dydx
: 2. Repeatedly throw a dice until two even numbers occur in a row or number
: is 3 or 5. What's probability of
: stopping by two consecutive numbers before 3 or 5?
: 3. Stock price is 100, strike is 100, maturity is 1 year. Current call price
: is 10. Assume you can buy/sell put or
: call, borrow/lend cash, purchase stock. But you can't sell stock!!. Please
: give tight bound of put option with
: the same strike and maturity.
: 4. Currently stock price X(0) = 100. Maturity is 1 year.
|
m*********g
发帖数: 646 | 4 2. Stop by two consecutive even number: P=1/3 |
m*********g
发帖数: 646 | 5 5. 就是change of numeraire 在 P-measure下的DYNAMICS吧
drift: U_X-U_Y+\sigma_Y^2
Vol: || \sigma_X-\sigma_Y ||
请大牛来确认。另外1的X的积分下限确认是 -inf 么？ |
j********t
发帖数: 97 | 6 是CS。
第三题就是已知ATM call，不允许sell stock，求put的上下界。 |
k*******d
发帖数: 1340 | 7 恩，我也算了一下， 是的
P = 1/6 P + 1/2 (1/2+1/6 P)
一开始糊涂了。。
【在 m*********g 的大作中提到】
: 2. Stop by two consecutive even number: P=1/3
|
u****g
发帖数: 402 | 8
应该是改变积分顺序，但有个负无穷不知道怎么办
number
是（3，5），还是 （3,3），（3,5），（5,5） （5,3）都可以？
用Markov Chain
price
Please
NO idea.
Put call parity should be still valid.
Same price. Using reflection principle.
【在 j********t 的大作中提到】
: 1. Calculate \int_{-\infty}^{\infty} \int_{x}^{\infty} xe^{y^3} dydx
: 2. Repeatedly throw a dice until two even numbers occur in a row or number
: is 3 or 5. What's probability of
: stopping by two consecutive numbers before 3 or 5?
: 3. Stock price is 100, strike is 100, maturity is 1 year. Current call price
: is 10. Assume you can buy/sell put or
: call, borrow/lend cash, purchase stock. But you can't sell stock!!. Please
: give tight bound of put option with
: the same strike and maturity.
: 4. Currently stock price X(0) = 100. Maturity is 1 year.
|
j********t
发帖数: 97 | 9 第二题是（3,3），（3,5），（5,5） （5,3）都可以。 |
u****g
发帖数: 402 | 10 2. Two even numbers occur first P = 2/3 |
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m*********g
发帖数: 646 | 11 啥 ？
我怎么觉得题意 是在问 ，你弄一个 3 出来，停；或者你弄一个5出来停。这两个为事
件1。你连续两次出EVEN number停 ，这个事件为 事件2
问概率：事件2 发生在 事件1之前 ？
【在 j********t 的大作中提到】
: 第二题是（3,3），（3,5），（5,5） （5,3）都可以。
|
d**********9
发帖数: 5215 | 12 i have the same understanding.
【在 m*********g 的大作中提到】
: 啥 ？
: 我怎么觉得题意 是在问 ，你弄一个 3 出来，停；或者你弄一个5出来停。这两个为事
: 件1。你连续两次出EVEN number停 ，这个事件为 事件2
: 问概率：事件2 发生在 事件1之前 ？
|
l*********t
发帖数: 89 | 13 补充一下，U_t and V_t are BM with correlation coefficient \rho.
【在 j********t 的大作中提到】
: 第二题是（3,3），（3,5），（5,5） （5,3）都可以。
|
l*********t
发帖数: 89 | 14 Agree with this.
【在 m*********g 的大作中提到】
: 啥 ？
: 我怎么觉得题意 是在问 ，你弄一个 3 出来，停；或者你弄一个5出来停。这两个为事
: 件1。你连续两次出EVEN number停 ，这个事件为 事件2
: 问概率：事件2 发生在 事件1之前 ？
|
m*********g
发帖数: 646 | 15 那vol 就是 sqrt(sig_x^2+sig_y^2-2*rho*sig_x*sig_y)
volatility
【在 l*********t 的大作中提到】
: 补充一下，U_t and V_t are BM with correlation coefficient \rho.
|
l*********t
发帖数: 89 | 16 why your drift does not include sigma_X?
【在 m*********g 的大作中提到】
: 5. 就是change of numeraire 在 P-measure下的DYNAMICS吧
: drift: U_X-U_Y+\sigma_Y^2
: Vol: || \sigma_X-\sigma_Y ||
: 请大牛来确认。另外1的X的积分下限确认是 -inf 么？
|
m*********g
发帖数: 646 | 17 Should it be there?
【在 l*********t 的大作中提到】
: why your drift does not include sigma_X?
|
p******e
发帖数: 756 | 18 第4题， option2岂不是确定的pay $1,因为s(0)〉90。
reflection principle这里可以用么，stock price并不是brownian motion
【在 u****g 的大作中提到】
: 2. Two even numbers occur first P = 2/3
|
j********t
发帖数: 97 | 19 对，原题就是你这个意思。
【在 m*********g 的大作中提到】
: 啥 ？
: 我怎么觉得题意 是在问 ，你弄一个 3 出来，停；或者你弄一个5出来停。这两个为事
: 件1。你连续两次出EVEN number停 ，这个事件为 事件2
: 问概率：事件2 发生在 事件1之前 ？
|
l*********t
发帖数: 89 | 20 I think drift should be
U_X-U_Y+\sigma_Y^2-\rho*sigma_X*sigma_Y
【在 m*********g 的大作中提到】
: Should it be there?
|
|
|
m*******r
发帖数: 4468 | 21 chance of two even in a row 1/3x1/3= 1/9
conditional probality the number is not 3 or 5.
indepedent events,
1/9 x 2/3=2/27
is this correct?
2. Repeatedly throw a dice until two even numbers occur in a row or number
is 3 or 5. What's probability of
stopping by two consecutive numbers before 3 or 5? |
M********t
发帖数: 163 | 22 对的
【在 m*********g 的大作中提到】
: 2. Stop by two consecutive even number: P=1/3
|
M********t
发帖数: 163 | 23 5 vol sqrt(sigma_X^2 + sigma_Y^2 - 2 * rho * sigma_X * sigma_Y)
【在 m*********g 的大作中提到】
: 5. 就是change of numeraire 在 P-measure下的DYNAMICS吧
: drift: U_X-U_Y+\sigma_Y^2
: Vol: || \sigma_X-\sigma_Y ||
: 请大牛来确认。另外1的X的积分下限确认是 -inf 么？
|
m**********4
发帖数: 774 | 24 For question 2, I got 1/3
In fact, you only need to compute P(win) and P(win|X1=2 or 4 or 6)
Who knows how to do question 1?
price
【在 j********t 的大作中提到】
: 1. Calculate \int_{-\infty}^{\infty} \int_{x}^{\infty} xe^{y^3} dydx
: 2. Repeatedly throw a dice until two even numbers occur in a row or number
: is 3 or 5. What's probability of
: stopping by two consecutive numbers before 3 or 5?
: 3. Stock price is 100, strike is 100, maturity is 1 year. Current call price
: is 10. Assume you can buy/sell put or
: call, borrow/lend cash, purchase stock. But you can't sell stock!!. Please
: give tight bound of put option with
: the same strike and maturity.
: 4. Currently stock price X(0) = 100. Maturity is 1 year.
|
m*********g
发帖数: 646 | 25 我觉得1的X积分下限有问题。。
【在 m**********4 的大作中提到】
: For question 2, I got 1/3
: In fact, you only need to compute P(win) and P(win|X1=2 or 4 or 6)
: Who knows how to do question 1?
:
: price
|
m*********g
发帖数: 646 | |
m**********4
发帖数: 774 | 27 Really? Why?
Sigh, no one talks about q1
【在 m*********g 的大作中提到】
: 我觉得1的X积分下限有问题。。
|
M********t
发帖数: 163 | 28 积分界限是 0 到 2； x 到 2。
无穷积分不收敛。
【在 m**********4 的大作中提到】
: Really? Why?
: Sigh, no one talks about q1
|
m*********g
发帖数: 646 | 29 then, it is (e^8-1)/6
【在 M********t 的大作中提到】
: 积分界限是 0 到 2； x 到 2。
: 无穷积分不收敛。
|
k****o
发帖数: 11 | 30 这道题joshi的书里有。2.15
on
【在 m*********g 的大作中提到】
: 讨论一下第四题：
|
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p******e
发帖数: 756 | 31 能大概讲一下思路么，手头没这本。。。
或者哪有电子版看一下。。。thx
【在 k****o 的大作中提到】
: 这道题joshi的书里有。2.15
:
: on
|
k****o
发帖数: 11 | 32 如果是brownian motion，由于reflection principle，两者价格应该是一样的。
但是换成gbm，就会有skew，导致pay2块的更贵。
【在 p******e 的大作中提到】
: 能大概讲一下思路么，手头没这本。。。
: 或者哪有电子版看一下。。。thx
|
t******7
发帖数: 31 | 33 假设r=0.如果S是arithmetic BM，那么如果在时间t<1达到90，那么在时间1,有50%的概
率>90。如果S是GBM，median是exp{r-1/2\sigma^2},小于90，所以S>90的概率要小于50
%.所以一块钱那个要贵。
请教下大牛这样解释对吧？然后还想请教下第3题该是什么思路啊？谢谢~ |
p******e
发帖数: 756 | 34 如果是gbm，是不是应该取决于drift的大小和方向，pay2块的最后ITM的概率不一定超过
50%吧。还是说assume r=0，那么drift就是负的
另外这个题用reflection principle感觉不合适吧，因为s（0）〉90，所以不一定找到
一个时刻，hit到90吧。即使是BM，option2的payoff 1 with prob 1，而option 1的pa
yoff with prob 〉50%，correct me if i am wrong， thx
【在 k****o 的大作中提到】
: 如果是brownian motion，由于reflection principle，两者价格应该是一样的。
: 但是换成gbm，就会有skew，导致pay2块的更贵。
|
b******e
发帖数: 118 | 35 Could you please explain it in detail? Thanks a lot!
【在 m**********4 的大作中提到】
: For question 2, I got 1/3
: In fact, you only need to compute P(win) and P(win|X1=2 or 4 or 6)
: Who knows how to do question 1?
:
: price
|
s*********n
发帖数: 237 | 36 The numerical seems not agree on it.
【在 m*********g 的大作中提到】
: then, it is (e^8-1)/6
|
s*********n
发帖数: 237 | 37 For 3, we can hedge the put with a portfolio (1. short a call, 2. long a
bond, 3. long a stock) by call-put parity.
This gives the final payoff 0 and therefore must price 0. Then the price is
fixed. Am I right?
price
year.
【在 j********t 的大作中提到】
: 1. Calculate \int_{-\infty}^{\infty} \int_{x}^{\infty} xe^{y^3} dydx
: 2. Repeatedly throw a dice until two even numbers occur in a row or number
: is 3 or 5. What's probability of
: stopping by two consecutive numbers before 3 or 5?
: 3. Stock price is 100, strike is 100, maturity is 1 year. Current call price
: is 10. Assume you can buy/sell put or
: call, borrow/lend cash, purchase stock. But you can't sell stock!!. Please
: give tight bound of put option with
: the same strike and maturity.
: 4. Currently stock price X(0) = 100. Maturity is 1 year.
|
m*********g
发帖数: 646 | 38 in ur code, shouldn't it be: {y, x, 2} ? not -x
it seems to be a very basic integral, didn't take too many steps to get [exp
(8)-1]/6
【在 s*********n 的大作中提到】
: The numerical seems not agree on it.
|
H******9
发帖数: 1180 | 39 Have you graduated yet?
【在 d*j 的大作中提到】
: CS 的考试？
:
: price
|
t**********a
发帖数: 166 | 40 This is the case for hedging short put position.
For long put position, you need to dynamic delta hedging (delta is positive,
no need to short).
Thus the option price can be priced "normally"
is
【在 s*********n 的大作中提到】
: For 3, we can hedge the put with a portfolio (1. short a call, 2. long a
: bond, 3. long a stock) by call-put parity.
: This gives the final payoff 0 and therefore must price 0. Then the price is
: fixed. Am I right?
:
: price
: year.
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s*********n
发帖数: 237 | 41 I am confused. I thought what I tried is to hedge a long put.
After all, what would be the answer? Normal put price?
positive,
【在 t**********a 的大作中提到】
: This is the case for hedging short put position.
: For long put position, you need to dynamic delta hedging (delta is positive,
: no need to short).
: Thus the option price can be priced "normally"
:
: is
|
T*******t
发帖数: 9274 | 42 第三题很考概念啊，借来问人去....
price
【在 j********t 的大作中提到】
: 对，原题就是你这个意思。
|
h********e
发帖数: 1972 | 43 我这个炒股的来答答第三题。。
put上届100下届10.
10以下的：买一个put 卖一个call，借10000买100股。（这里要假设0利率）
100以上：卖一个put，留10000下来存银行，其他的当零花钱。
【在 T*******t 的大作中提到】
: 第三题很考概念啊，借来问人去....
:
: price
|
