e*******d
发帖数: 740 | 1 1. Knowing call price and strike price, how to identify the density function
in risk neutral world.
2. Let us say that we play a game in which we generate a random walk, and
every time the walk is positive you pay me some amount, but as soon as the
walk becomes negative the first time, I am out and we no longer play. How
does the probability of me staying in the game behave asymptotically after
very many steps?
3. The IBM stock is trading today at 100 and pays no dividends. Let us now
assume fo |
a**m
发帖数: 102 | 2 1. 条件是不是说知道call price可以写成strike price的函数啊？
2. 用reflection principle就可以了。
3. 什么是algebraic brownian motion啊？
function
us
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【在 e*******d 的大作中提到】
: 1. Knowing call price and strike price, how to identify the density function
: in risk neutral world.
: 2. Let us say that we play a game in which we generate a random walk, and
: every time the walk is positive you pay me some amount, but as soon as the
: walk becomes negative the first time, I am out and we no longer play. How
: does the probability of me staying in the game behave asymptotically after
: very many steps?
: 3. The IBM stock is trading today at 100 and pays no dividends. Let us now
: assume fo
|
r*******s
发帖数: 303 | 3 1.
c = exp(-rt) E(Max(s-k))
= exp(-rt) Int_k^inf (s-k) f(s) ds
对k求两次导，解出 f(s).
2.
gambler's ruin.
3.
dS = const * dW
P(stock goes below 80 at ANY time ) = 2P(stock ends up below 80)
[reflection principle. see the cover of Shreve.]
价格是 $0.17*2 |
e*******d
发帖数: 740 | 4 1.题目的前半问是Knowing the density function in risk neutral world and
strike K, how to compute the call price.这后半问只是反过来了。我想只用
describe一下如何做，不用给具体的函数。
2.什么是reflection principle? 这里如何apply？
3.algebraic brownian motion: 我觉得意思就是stock price +/- brownian
distribution 而不是 dp/p +/- brownian. |
p*****k
发帖数: 318 | 5 since redtulip has already given the answers, just
couple of references:
1. also known as strike gamma: d^2 C/(d K)^2
see Haug (the collector)'s book about probability greeks.
2. a similar problem was discussed here a while ago:
http://www.mitbbs.com/article_t/Quant/31217709.html
3. i think the more standard term is:
"arithmetic brownian motion"
once you understand 2, this should be easy. |
e*******d
发帖数: 740 | 6 有没有哪位老大给一下第2题的做法，我实在是不知道reflection principle在这里怎
么用。 |
r*******s
发帖数: 303 | 7 不用reflection.
p=1.
random walk has probability 1 to reach any point.
或者用gambler's ruin,
start at 0, stop at -m or +n.
到 -m 的概率是 n/(m+n).
在你的题目中， m=1, n=+inf.
probability of reach -1 is (inf)/(inf+1) =1.
【在 e*******d 的大作中提到】
: 有没有哪位老大给一下第2题的做法，我实在是不知道reflection principle在这里怎
: 么用。
|
e*******d
发帖数: 740 | 8 你是说p=1/2吗？但对general p有没有可能写出表达式来。
【在 r*******s 的大作中提到】
: 不用reflection.
: p=1.
: random walk has probability 1 to reach any point.
: 或者用gambler's ruin,
: start at 0, stop at -m or +n.
: 到 -m 的概率是 n/(m+n).
: 在你的题目中， m=1, n=+inf.
: probability of reach -1 is (inf)/(inf+1) =1.
|
a**m
发帖数: 102 | 9 I do not think 2 is about gambler's ruin.
【在 r*******s 的大作中提到】
: 1.
: c = exp(-rt) E(Max(s-k))
: = exp(-rt) Int_k^inf (s-k) f(s) ds
: 对k求两次导，解出 f(s).
: 2.
: gambler's ruin.
: 3.
: dS = const * dW
: P(stock goes below 80 at ANY time ) = 2P(stock ends up below 80)
: [reflection principle. see the cover of Shreve.]
|
