p**e
发帖数: 41 | 1 可能大家见过， 我想了想还是做不出来， 希望大家帮忙提示一下：
1， for the same stock, there are three option prices in mkt: C(K=10)=5, P(
K=12)=4, C(K=14)=3, the question is: is there any arbitrage opptunity?
2, Alice keeps tossing a fair coin until she gets 2 consecutive heads,
Define X as the number of tosses for this process. Bob keeps tossing another
fair coin until he gets 3 consecutive heads, and Define Y as the number of
tossed for Bob's process. Question: what is the probability of X>Y ? |
p**e
发帖数: 41 | 2 why Apparently the payoff of these two portfolios is totally different ? it
is possible that the payoff of them are equal, I think.
opportunity"
price |
p**e
发帖数: 41 | 3 我是说有可能你说的两个portfolio的payoff相等啊。
比如， c（k＝10）与c（k＝14）的pf的payoff是过点（10，0），（14，4）的slope为
1的线段加上过点（14，4），（16，8）的线段的组成，
而2个p（k＝12）的pf的payoff是过点（10，4），（12，0）的slope为－2的线段，
显然这两个payoff可以在点（34/3，4/3）相交， 也就是在stock price为34/3=11.
3333时候，两个portfolio的payoff相同啊。
hints. |
r**a
发帖数: 536 | 4 Sorry, I made mistake on calculation. Yes, you are right. My portfolio can't
show that there exists any arbitrage opportunities. Sorry for the confusion
. |
c*********n
发帖数: 128 | 5 第一个题目是不是转述错了？三个都是C？
如果三个都是C的话，那么有arbitrage，因为两个K=12的pay off跟一个K=10加一个K=
14的payoff不一样，前者多出来一小块，所以应该更贵。
如果第二个是P，那么我看不出来这里有什么inconsistency。
P(
another
of
【在 p**e 的大作中提到】
: 可能大家见过， 我想了想还是做不出来， 希望大家帮忙提示一下：
: 1， for the same stock, there are three option prices in mkt: C(K=10)=5, P(
: K=12)=4, C(K=14)=3, the question is: is there any arbitrage opptunity?
: 2, Alice keeps tossing a fair coin until she gets 2 consecutive heads,
: Define X as the number of tosses for this process. Bob keeps tossing another
: fair coin until he gets 3 consecutive heads, and Define Y as the number of
: tossed for Bob's process. Question: what is the probability of X>Y ?
|
c*********n
发帖数: 128 | 6 第二个用Markovian Chain，就是state稍微多了点，有八个：
0 - A:T, B:T
1 - A:T, B:H
2 - A:T, B:HH
3 - B:HHH
4 - A:H, B:T
5 - A:H, B:H
6 - A:H, B:HH
7 - A:HH
其中3和7是absorbing state，各个point之间的conversion prob都可以写出来，然后
列个8元一次方程组计算最后收敛到7的概率就是X>Y的概率。
P(
another
of
【在 p**e 的大作中提到】
: 可能大家见过， 我想了想还是做不出来， 希望大家帮忙提示一下：
: 1， for the same stock, there are three option prices in mkt: C(K=10)=5, P(
: K=12)=4, C(K=14)=3, the question is: is there any arbitrage opptunity?
: 2, Alice keeps tossing a fair coin until she gets 2 consecutive heads,
: Define X as the number of tosses for this process. Bob keeps tossing another
: fair coin until he gets 3 consecutive heads, and Define Y as the number of
: tossed for Bob's process. Question: what is the probability of X>Y ?
|
k***n
发帖数: 997 | 7 这些状态是怎么找的？
这个马可夫链的转移矩阵是什么？
【在 c*********n 的大作中提到】
: 第二个用Markovian Chain，就是state稍微多了点，有八个：
: 0 - A:T, B:T
: 1 - A:T, B:H
: 2 - A:T, B:HH
: 3 - B:HHH
: 4 - A:H, B:T
: 5 - A:H, B:H
: 6 - A:H, B:HH
: 7 - A:HH
: 其中3和7是absorbing state，各个point之间的conversion prob都可以写出来，然后
|
I******4
发帖数: 5 | 8 同意你的做法，8个状态 = 3 * 2 + 1 + 1
只不过要注意在merge状态的时候，A:HH & B:HHH 的状态（即同时实现）要 merge 到
HH 中去。
【在 c*********n 的大作中提到】
: 第二个用Markovian Chain，就是state稍微多了点，有八个：
: 0 - A:T, B:T
: 1 - A:T, B:H
: 2 - A:T, B:HH
: 3 - B:HHH
: 4 - A:H, B:T
: 5 - A:H, B:H
: 6 - A:H, B:HH
: 7 - A:HH
: 其中3和7是absorbing state，各个point之间的conversion prob都可以写出来，然后
|
x********9
发帖数: 31 | 9 There is an arbitrage opportunity.
What you should consider is long the 2 Calls and short 2* the put, and short
2 contracts of future.
at t=0:
2*4-5-3 = 0
at maturity:
you get a butterfly(the reverse of butterfly, I forgot the name) or so for
free. |
u********h
发帖数: 146 | 10 没看懂。。。
short
【在 x********9 的大作中提到】
: There is an arbitrage opportunity.
: What you should consider is long the 2 Calls and short 2* the put, and short
: 2 contracts of future.
: at t=0:
: 2*4-5-3 = 0
: at maturity:
: you get a butterfly(the reverse of butterfly, I forgot the name) or so for
: free.
|
|
|
c**v
发帖数: 55 | 11 it's easy to see the arbitrage by long c(k=10) & c(k=14) and short 2 c(k=12).
according to put-call parity, c(k=12) can be replicated by p(k=12) and
its underlying. so if ignoring the cost of lending underlying, arbitrage
exist.
【在 u********h 的大作中提到】
: 没看懂。。。
:
: short
|
r**a
发帖数: 536 | 12
12).
Why? long c(k=10) & c(k=14) and short 2 c(k=12) will get a butterfly payoff.
But why should there be an arbitrage opportunity? Unless you can confirm
that c(k=14)+c(k=10)-2c(k=12)<=0. But I did not see how you prove this
inequality.
【在 c**v 的大作中提到】
: it's easy to see the arbitrage by long c(k=10) & c(k=14) and short 2 c(k=12).
: according to put-call parity, c(k=12) can be replicated by p(k=12) and
: its underlying. so if ignoring the cost of lending underlying, arbitrage
: exist.
|
x******a
发帖数: 6336 | 13 call price is a convex function of k.
payoff.
【在 r**a 的大作中提到】
:
: 12).
: Why? long c(k=10) & c(k=14) and short 2 c(k=12) will get a butterfly payoff.
: But why should there be an arbitrage opportunity? Unless you can confirm
: that c(k=14)+c(k=10)-2c(k=12)<=0. But I did not see how you prove this
: inequality.
|
c**v
发帖数: 55 | 14 my bad. my idea is: there is arbitrage WHEN lending cost is less-equal to
zero.
c(k=14)+c(k=10)-2c(k=12) = 2*[ 12*B(t,T)-S(t)].
it's lending shares and buying bonds, and arbitrage exists when market price
is greater-equal to 12*B(t,T).
payoff.
【在 r**a 的大作中提到】
:
: 12).
: Why? long c(k=10) & c(k=14) and short 2 c(k=12) will get a butterfly payoff.
: But why should there be an arbitrage opportunity? Unless you can confirm
: that c(k=14)+c(k=10)-2c(k=12)<=0. But I did not see how you prove this
: inequality.
|
r**a
发帖数: 536 | 15 I totally agree with you. But in the original question, there is no any info
about S(t). So I do not think you can say that there must be an arbitrage
opportunity.
price
【在 c**v 的大作中提到】
: my bad. my idea is: there is arbitrage WHEN lending cost is less-equal to
: zero.
: c(k=14)+c(k=10)-2c(k=12) = 2*[ 12*B(t,T)-S(t)].
: it's lending shares and buying bonds, and arbitrage exists when market price
: is greater-equal to 12*B(t,T).
:
: payoff.
|
r**a
发帖数: 536 | 16
of course. The 2nd derivative of call w.r.t. strike is related to the
transition probability of the stock. So it must be positive, otherwise there
will be an arbitrage opportunity. But from the numbers of this question, at
least I can NOT conclude that the 2nd derivative of call is not positive.
So I can NOT conclude anything about whether there must exist an arbitrage
opportunity, unless the present values of the stock and bond are known.
【在 x******a 的大作中提到】
: call price is a convex function of k.
:
: payoff.
|
c**v
发帖数: 55 | 17 In my opinion, if I have PROBABILITY to get something for free, there exist
arbitrage OPPORTUNITY.
As neither of us know S(t), we are unable to exclude the possibility of
getting free cake, so the opportunity exists, right?
my bad for being long-winded, I am recently becoming a fan of philosophy -.-
info
【在 r**a 的大作中提到】
: I totally agree with you. But in the original question, there is no any info
: about S(t). So I do not think you can say that there must be an arbitrage
: opportunity.
:
: price
|
e****0
发帖数: 378 | 18 1 no arbitrage opportunity
P(
another
of
【在 p**e 的大作中提到】
: 可能大家见过， 我想了想还是做不出来， 希望大家帮忙提示一下：
: 1， for the same stock, there are three option prices in mkt: C(K=10)=5, P(
: K=12)=4, C(K=14)=3, the question is: is there any arbitrage opptunity?
: 2, Alice keeps tossing a fair coin until she gets 2 consecutive heads,
: Define X as the number of tosses for this process. Bob keeps tossing another
: fair coin until he gets 3 consecutive heads, and Define Y as the number of
: tossed for Bob's process. Question: what is the probability of X>Y ?
|
r**a
发帖数: 536 | 19
exist
I do not think your statement is the same as the usual one. The common sense
/definition of the arbitrage opportunity can be found in the book "theory of
financial decision making" by Ingersoll page 28.
.-
【在 c**v 的大作中提到】
: In my opinion, if I have PROBABILITY to get something for free, there exist
: arbitrage OPPORTUNITY.
: As neither of us know S(t), we are unable to exclude the possibility of
: getting free cake, so the opportunity exists, right?
: my bad for being long-winded, I am recently becoming a fan of philosophy -.-
:
: info
|
r**a
发帖数: 536 | 20 why?
【在 e****0 的大作中提到】
: 1 no arbitrage opportunity
:
: P(
: another
: of
|
c**v
发帖数: 55 | 21 我被你打败了。。。
my last word, opportunity favors those who appreciate it.
sense
of
【在 r**a 的大作中提到】
: why?
|
