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Quant版 - Interview questions
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1 (共1页)
x*********u
发帖数: 66
1
1.For the same stock, the price of call option with strike price $10 is $5.
the price of put option with strike price $12 is $4. The price of call
option with strike price $14 is $3. Is there any arbitrage?
2. There is a sever and finite number of computers. Each computer contains a
data set. The data set may overlap each other. How to find a median of the
whole large data set?
Any idea?
d*j
发帖数: 13780
2
GS
good luck
g****y
发帖数: 71
3
1. should depend on the spot price i guess.
don't know about 2.
s********7
发帖数: 52
4
1 butterfly
2 hashtable
J*****n
发帖数: 4859
5

第一个无法用butterfly的,因为中间那个是Put price,你不知道是否over or under
priced.

【在 s********7 的大作中提到】
: 1 butterfly
: 2 hashtable

z*********r
发帖数: 298
6
Sell those two calls and puts, when the price is between 8 to 16 you have an
earning
J*****n
发帖数: 4859
7

an
你这不叫arbitrage。

【在 z*********r 的大作中提到】
: Sell those two calls and puts, when the price is between 8 to 16 you have an
: earning

z*********r
发帖数: 298
8
Sorry, should be Buy those call and puts and enjoy an arbitrage of $2

an

【在 z*********r 的大作中提到】
: Sell those two calls and puts, when the price is between 8 to 16 you have an
: earning

J*****n
发帖数: 4859
9

也不对
你全买,花了12块(5+4+3),假如你的股票价格停留在12块的话,你只有strike 10的
期权赚两块,最后你还亏10块。

【在 z*********r 的大作中提到】
: Sorry, should be Buy those call and puts and enjoy an arbitrage of $2
:
: an

z*********r
发帖数: 298
10
股票的价格是6快,你算一下就出来了
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进入Quant版参与讨论
J*****n
发帖数: 4859
11

你怎么算的?

【在 z*********r 的大作中提到】
: 股票的价格是6快,你算一下就出来了
z*********r
发帖数: 298
12
用Put Call Parity
J*****n
发帖数: 4859
13

连strike都不一样,怎么用put call parity?

【在 z*********r 的大作中提到】
: 用Put Call Parity
z*********r
发帖数: 298
14
我Assume两个Call和起来的Strike是12
m*****n
发帖数: 3575
15
short two puts
buy both calls
short two futures
the set up cost is 0
there is a positive bump between 10 and 14, 0 otherwise
a**m
发帖数: 102
16
what's the futures price you assume?

【在 m*****n 的大作中提到】
: short two puts
: buy both calls
: short two futures
: the set up cost is 0
: there is a positive bump between 10 and 14, 0 otherwise

d*j
发帖数: 13780
17
有道理啊,short stock 起码要知道现在的 stock price

【在 a**m 的大作中提到】
: what's the futures price you assume?
d*j
发帖数: 13780
18
1.For the same stock, the price of call option with strike price $10 is $5.
the price of put option with strike price $12 is $4.
光看这个就知道不合理了
call 10$ strike at 5$, 说明股票价格 15$ 左右
put 12$ at 4$ 说明股票价格 8$ 左右, 呵呵

.
a
the

【在 x*********u 的大作中提到】
: 1.For the same stock, the price of call option with strike price $10 is $5.
: the price of put option with strike price $12 is $4. The price of call
: option with strike price $14 is $3. Is there any arbitrage?
: 2. There is a sever and finite number of computers. Each computer contains a
: data set. The data set may overlap each other. How to find a median of the
: whole large data set?
: Any idea?

s*****y
发帖数: 33
19
I think it depends on moneyness. consider the price curve of call options.
it is convex, so call(12)<4=put(12). c-p<0 there is arbitrage if s>e{-rT}*
K

.
a
the

【在 x*********u 的大作中提到】
: 1.For the same stock, the price of call option with strike price $10 is $5.
: the price of put option with strike price $12 is $4. The price of call
: option with strike price $14 is $3. Is there any arbitrage?
: 2. There is a sever and finite number of computers. Each computer contains a
: data set. The data set may overlap each other. How to find a median of the
: whole large data set?
: Any idea?

x*********u
发帖数: 66
20
Buy all of them. Call option has unlimited profit and limited loss. Put
option has also limited loss. So if two call options are deep in the money,
there exists a positive profit. That means if stock price is bigger than $18
, you earn more than $12,which can cover your initial cost $12. Am I right?

【在 J*****n 的大作中提到】
:
: 连strike都不一样,怎么用put call parity?

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m*****n
发帖数: 3575
21
It's irrelavent, just choose the future that cost you 0, Sexp(rt)

【在 a**m 的大作中提到】
: what's the futures price you assume?
m*****n
发帖数: 3575
22
哎,我这么水平高的人都留不下!!!
你们几个要是还不懂,画个图就懂了。
w*****e
发帖数: 197
23
You are really good. I can see how to use the strike 10 and 14
calls to replicate 2 strike 12 calls. But I did not realize
that gave me exactly the arb I needed. Thanks a lot!

【在 m*****n 的大作中提到】
: short two puts
: buy both calls
: short two futures
: the set up cost is 0
: there is a positive bump between 10 and 14, 0 otherwise

s*******1
发帖数: 20
24
I guess you S is S_0. Could you explain what happens when S_T<10 for your
portfolio? Thanks.

【在 m*****n 的大作中提到】
: It's irrelavent, just choose the future that cost you 0, Sexp(rt)
m*****n
发帖数: 3575
25
I am sorry for the mistake made in the previous post.
Actually the arbitrage needs a condition that future quote is 12 NOW.
Thus, the butterfly can sit on x horizon in the future.
If price falls below 10, both calls are abandoned.2 Puts are exercised that
you need to pay 2*12 dollars for the stocks. And these stocks should be sold
to redeem the two futures short.The cash inflow from this sell is 2F, which
is 24 is F was 12 in t=0.
If price goes between 10 and 12, two puts cancells two futures if
m*****n
发帖数: 3575
26
The arbitrage holds if the future 12 is priced at 0 today.
Sexp(rt)=12.
a**m
发帖数: 102
27
So you need this assumption anyway, although this is something interviewer
did not provide...

【在 m*****n 的大作中提到】
: The arbitrage holds if the future 12 is priced at 0 today.
: Sexp(rt)=12.

1 (共1页)
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话题: price话题: strike话题: call话题: 12话题: arbitrage