b*****g
发帖数: 23 | 1 A stock is trading at $45 today. What is the value of an option that pays
off $1 if the stock ever rises above $100? (assume interest rates are zero) |
s*******s
发帖数: 1568 | 2 45/100 by non-arbitrary
【在 b*****g 的大作中提到】
: A stock is trading at $45 today. What is the value of an option that pays
: off $1 if the stock ever rises above $100? (assume interest rates are zero)
|
m******2
发帖数: 252 | 3 45/100
if interest rate is 0,then under risk-neutral measure，stock price is a
martingale: dS_t = S_t Sigma_t dW_t
Then Price = E^Q(I_{S_t到达0之前先到达100}) = P(S_t到达0之前先到达100) = 45/100
(last equation comes from the martingale property)
【在 b*****g 的大作中提到】
: A stock is trading at $45 today. What is the value of an option that pays
: off $1 if the stock ever rises above $100? (assume interest rates are zero)
|
n****e
发帖数: 629 | 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
How come? Assuming you're in a risk-neutral measure
【在 m******2 的大作中提到】
: 45/100
: if interest rate is 0,then under risk-neutral measure，stock price is a
: martingale: dS_t = S_t Sigma_t dW_t
: Then Price = E^Q(I_{S_t到达0之前先到达100}) = P(S_t到达0之前先到达100) = 45/100
: (last equation comes from the martingale property)
:
|
n****e
发帖数: 629 | 5 When the stock vol!=0...
Otherwise it's worthless, hehe
【在 s*******s 的大作中提到】
: 45/100 by non-arbitrary
|
m******2
发帖数: 252 | 6 sorry, my bad, it should be attaining 100 before 0.
【在 n****e 的大作中提到】
: When the stock vol!=0...
: Otherwise it's worthless, hehe
|
b*****g
发帖数: 23 | 7 so the price will rise over 100 with probability 1? |
d*j
发帖数: 13780 | 8 想想就知道了
用 replication
在t_0 的时候买入 1/100 份 股票
等到了 T , S=100 的时候卖掉
那么这个东西在 t_0 是多少钱？
【在 b*****g 的大作中提到】
: A stock is trading at $45 today. What is the value of an option that pays
: off $1 if the stock ever rises above $100? (assume interest rates are zero)
|
x**y
发帖数: 10012 | 9 人才阿
我的想法是 出题的不会很难 否则考生不能在几分钟内做出来
所以得是很快出答案的
所以只能是100和45这两数字得组合。。。
【在 d*j 的大作中提到】
: 想想就知道了
: 用 replication
: 在t_0 的时候买入 1/100 份 股票
: 等到了 T , S=100 的时候卖掉
: 那么这个东西在 t_0 是多少钱？
|
J****g
发帖数: 103 | 10 恩， 我还想着是binary option, 100N(d_2)呢 ：（
【在 d*j 的大作中提到】
: 想想就知道了
: 用 replication
: 在t_0 的时候买入 1/100 份 股票
: 等到了 T , S=100 的时候卖掉
: 那么这个东西在 t_0 是多少钱？
|
|
|
p*****k
发帖数: 318 | 11 bgcydrg, there was a very nice discussion about this problem yrs ago
on this board:
http://www.mitbbs.com/article_t/Quant/31178792.html
it is also discussed in Crack's book (problem 2.3), which might help
you understanding tradingGamma's comments better in the thread above.
generally the replication argument does work, though with caveat.
to see this, consider a variant:
the current stock price is above $100, e.g., it's $145.
same option: payoff is $1 when the stock ever hits $100.
what is this |
b*****g
发帖数: 23 | 12 That thread helps a lot. Thank you all for the help.
【在 p*****k 的大作中提到】
: bgcydrg, there was a very nice discussion about this problem yrs ago
: on this board:
: http://www.mitbbs.com/article_t/Quant/31178792.html
: it is also discussed in Crack's book (problem 2.3), which might help
: you understanding tradingGamma's comments better in the thread above.
: generally the replication argument does work, though with caveat.
: to see this, consider a variant:
: the current stock price is above $100, e.g., it's $145.
: same option: payoff is $1 when the stock ever hits $100.
: what is this
|
s****n
发帖数: 1237 | 13 但是如果S没有到达过100，原题的option pay off 0
这个replicating就不是0，而是S_T/100啊，难道不需要一样吗？
【在 d*j 的大作中提到】
: 想想就知道了
: 用 replication
: 在t_0 的时候买入 1/100 份 股票
: 等到了 T , S=100 的时候卖掉
: 那么这个东西在 t_0 是多少钱？
|
w*****e
发帖数: 197 | 14 As long as under your choice of measure, there is
a 0.8 chance of reaching 100, the answer is 0.8.
0.8 is just an upper bound out of static replication
like folks have pointed out, the real deal here is
to determine the lower bound. And the risk neutral
measure obviously gives a lower bound.
【在 s****n 的大作中提到】
: 但是如果S没有到达过100，原题的option pay off 0
: 这个replicating就不是0，而是S_T/100啊，难道不需要一样吗？
|
w*****e
发帖数: 197 | 15 I thought this one is actually in "heard on street"?
pays
zero)
【在 b*****g 的大作中提到】
: A stock is trading at $45 today. What is the value of an option that pays
: off $1 if the stock ever rises above $100? (assume interest rates are zero)
|
