h*****u
发帖数: 204 | 1 On page 228 Shreve II:
Definition 5.4.3 A probability measure Q is said to be risk neutral if
(i) Q is equivalent to P.
(ii) Under Q, the discounted stock price is a martingale.
My question: He uses the discount stock price is a martingale,
why not the discount portfolio is a martingale?
My comment: From my experience, we usually use the risk neutral measure to
compute the option price.(?? Is this right?)
But in section 5.5 dividend-paying stocks,(page234-237) he said under the
risk neutral measure, the discounted stock price is not a martingale.(How
does this make sense???)
Thanks. | A*****s
发帖数: 13748 | 2
Discounted portfolio value, given there is no cost/benifit of carry, follows
a martingale too UNDER the Q measure. B-S derivation uses this fact.
Derivative price is the expected discounted payoff UNDER the Q measure. You
are right if this is what you mean by "use".
When there is a cost/benifit to carry, the drift of the security is no
longer risk free rate under Q measure. It should be r-q+c where q is benifit
rate and c is cost rate. Think of cost as an example, if the drift under RN
does not even reach r+c, why bother carrying it? why not just sell it and
put money into the Money Market?
【在 h*****u 的大作中提到】
: On page 228 Shreve II:
: Definition 5.4.3 A probability measure Q is said to be risk neutral if
: (i) Q is equivalent to P.
: (ii) Under Q, the discounted stock price is a martingale.
: My question: He uses the discount stock price is a martingale,
: why not the discount portfolio is a martingale?
: My comment: From my experience, we usually use the risk neutral measure to
: compute the option price.(?? Is this right?)
: But in section 5.5 dividend-paying stocks,(page234-237) he said under the
: risk neutral measure, the discounted stock price is not a martingale.(How
| h*****u
发帖数: 204 | 3 1 "Discounted portfolio value, given there is no cost/benifit of carry,
follows a martingale too UNDER the Q measure. B-S derivation uses this fact."
I think even if there is dividend/cost of carry, but the discounted
portfolio is still a martingale.
(if there is dividend/cost of carry, then the discounted stock price is not
martingale)
2 My comment: From my experience, we usually use the risk neutral measure
to
Derivative price is the expected discounted payoff UNDER the Q measure. You
are right if this is what you mean by "use".
but shreve section 5.5 he didn't use the risk neutral measure to compute the
option price, he used the measure such that the discounted portfolio is
martingale.
3 : On page 228 Shreve II:
My Question:
But in section 5.5 dividend-paying stocks,(page234-237) he said under the
risk neutral measure, the discounted stock price is not a martingale, is
this contradiction to the definition of risk neutral?
follows
You
benifit
RN | y******i
发帖数: 199 | 4 I think even if there is dividend/cost of carry, but the discounted
portfolio is still a martingale.
正确
but shreve section 5.5 he didn't use the risk neutral measure to compute
theoption price, he used the measure such that the discounted portfolio is
martingale.
这就是risk-neutral measure。如果所有asset的discounted value都是martingale，
那么用它们所组成的portfolio的discounted value也必定是martingale。
My Question:
But in section 5.5 dividend-paying stocks,(page234-237) he said under the
risk neutral measure, the discounted stock price is not a martingale, is
this contradiction to the definition of risk neutral?
你hold这个stock，把dividend和stock price的变化都算上，discounted value仍然是
martingale。risk neutral定义的本质是，你持有任何asset或者portfolio，
stochastic process of value has a drift of risk-free rate.
fact."
not
You
【在 h*****u 的大作中提到】
: 1 "Discounted portfolio value, given there is no cost/benifit of carry,
: follows a martingale too UNDER the Q measure. B-S derivation uses this fact."
: I think even if there is dividend/cost of carry, but the discounted
: portfolio is still a martingale.
: (if there is dividend/cost of carry, then the discounted stock price is not
: martingale)
: 2 My comment: From my experience, we usually use the risk neutral measure
: to
: Derivative price is the expected discounted payoff UNDER the Q measure. You
: are right if this is what you mean by "use".
|
|
