b***k
发帖数: 2673 | 1 ☆─────────────────────────────────────☆
geome (珍惜生命远离bbs) 于 (Tue Mar 4 11:29:45 2008) 提到:
1. put k balls into n boxes, whats the expectation of empty boxes.
2. r=0,price down-and-out options with strike=barrier
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fleurgarcon (fleurgarcon) 于 (Tue Mar 4 12:41:01 2008) 提到:
Have no idea of 2. But for 1, I think it can be worked out quite easily.
Let A_i be the event that the i-th box is empty, and X_i be the
characteristic function of A_i, then
E(# o | n**x
发帖数: 6 | 2 1. for the first question, I think fleurgarcon's answer is absolutely right.
2. for the second, I also think the price should be S0-K. We can proceed by
replicating the payoff of the barrier using vanilla calls and puts. If the
stock price is always higher than the barrier B (or K because B=K) during
the lifetime of the option, then it is a vanilla call struck at K. But if
the stock price once touches the barrier, the option should become zero in
value. Thus in our replicating portfolio we can j | q*s
发帖数: 26 | 3 What if it touches the boundary and rise back above the strike?
right.
by
money
【在 n**x 的大作中提到】
: 1. for the first question, I think fleurgarcon's answer is absolutely right.
: 2. for the second, I also think the price should be S0-K. We can proceed by
: replicating the payoff of the barrier using vanilla calls and puts. If the
: stock price is always higher than the barrier B (or K because B=K) during
: the lifetime of the option, then it is a vanilla call struck at K. But if
: the stock price once touches the barrier, the option should become zero in
: value. Thus in our replicating portfolio we can j
| n**x
发帖数: 6 | 4 To hedge the barrier option with the call and put, I mean you start with
longing the call option, and whenever the barrier is touched, you short a
put with the same strike,and dissolve the replication portofolio immediately
.So you portofolio immediately goes to zero value, that what the down-and-
out call option means. | i****e
发帖数: 78 | 5 the measure was already changed such that the BM in GBM is driftless.
n
【在 b***k 的大作中提到】
: ☆─────────────────────────────────────☆
: geome (珍惜生命远离bbs) 于 (Tue Mar 4 11:29:45 2008) 提到:
: 1. put k balls into n boxes, whats the expectation of empty boxes.
: 2. r=0,price down-and-out options with strike=barrier
: ☆─────────────────────────────────────☆
: fleurgarcon (fleurgarcon) 于 (Tue Mar 4 12:41:01 2008) 提到:
: Have no idea of 2. But for 1, I think it can be worked out quite easily.
: Let A_i be the event that the i-th box is empty, and X_i be the
: characteristic function of A_i, then
: E(# o
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