Q***5
发帖数: 994 | 1 From Crack's book, answer to 2.2:
"Option value decays toward kinked final payoff as expiration approaches.
This time decay is called theta. We usually think about theta as being
negative for plain vanilla options, but there are two clear exceptions. A
deep in-the-money European-style call can have positive theta if the
dividend yield is high enough--because high dividends can push price down
below intrinsic value and the option then has to 'decay upward' in value as
expiration approaches ...." |
T******r
发帖数: 257 | 2 option value --> payoff when t --> T
as
【在 Q***5 的大作中提到】
: From Crack's book, answer to 2.2:
: "Option value decays toward kinked final payoff as expiration approaches.
: This time decay is called theta. We usually think about theta as being
: negative for plain vanilla options, but there are two clear exceptions. A
: deep in-the-money European-style call can have positive theta if the
: dividend yield is high enough--because high dividends can push price down
: below intrinsic value and the option then has to 'decay upward' in value as
: expiration approaches ...."
|
Q***5
发帖数: 994 | 3 Yes, option value approaches the intrinsic value as t-->T, but in this case,
the intrinsic value decreases as dividend yield increases, should the
option value decrease from this perspective?
【在 T******r 的大作中提到】
: option value --> payoff when t --> T
:
: as
|
Q***5
发帖数: 994 | 4 Perhaps the author means to say:
Large dividend push CURRENT call option value toward 0, but since the call
is deeply in money, at maturity, the option price (equals the intrinsic
value) should be positive, therefore, theta should be positive.
If so, I think ThatYear's explanation is right: it is just about option value converges to intrinsic as t-->T
Still, it seems that the author assumes that as dividend increase, the call option value decrease -- but the intrinsic value at T does not decreas |
T*******t
发帖数: 9274 | 5 你手里有个in the money call...
假设stock没vol...但天天直线下跌...
你希望maturity早一天还是晚一天？ |
Q***5
发帖数: 994 | 6 In that case, the earlier the better -- i.e. theta is negative.
【在 T*******t 的大作中提到】
: 你手里有个in the money call...
: 假设stock没vol...但天天直线下跌...
: 你希望maturity早一天还是晚一天？
|
T*******t
发帖数: 9274 | 7 你搞清楚theta的定义了吗？
是dc/dt 还是dc/d(T-t)? |
Q***5
发帖数: 994 | 8 My understanding is dc/dt.
Can you explain using the example you provided, why theta should be positive?
【在 T*******t 的大作中提到】
: 你搞清楚theta的定义了吗？
: 是dc/dt 还是dc/d(T-t)?
|
T*******t
发帖数: 9274 | 9 当你说越短越好的时候，就是说
dc/d(T-t) < 0...所以 dc/dt > 0....
positive?
【在 Q***5 的大作中提到】
: My understanding is dc/dt.
: Can you explain using the example you provided, why theta should be positive?
|
Q***5
发帖数: 994 | 10 I see your point.
My reasoning was: suppose at some time t1
your assumption, the underline goes down, so at a later time t2>t1 (but t2
), c_t2
I guess we should not have used the example you gave: theta by definition
only considers the change of option price w.r.t time t, holding other
variables constant -- this includes holding stock price constant.
More specifically, let C(t,s_t) be the option price at time t with stock
price s_t.
【在 T*******t 的大作中提到】
: 当你说越短越好的时候，就是说
: dc/d(T-t) < 0...所以 dc/dt > 0....
:
: positive?
|
p*****k
发帖数: 318 | 11 this might a tautology:
my understanding is that with high dividend, it drives the option
price below its intrinsic value when it's deep-in-the-money,
(one way to see this is that Delta does not approach 1 fast enough
due to the extra exponential factor)
so there the time-value of the option becomes negative. since the
time-value approaches zero closer to the expiration, Theta becomes
positive.
i think sometimes ppl are also interested in the so-called
"driftless theta" by ignoring the discount |
Q***5
发帖数: 994 | 12 Thanks, I need to think more about what you said tomorrow..., for now I'm
just too sleepy to think straight.
【在 p*****k 的大作中提到】
: this might a tautology:
: my understanding is that with high dividend, it drives the option
: price below its intrinsic value when it's deep-in-the-money,
: (one way to see this is that Delta does not approach 1 fast enough
: due to the extra exponential factor)
: so there the time-value of the option becomes negative. since the
: time-value approaches zero closer to the expiration, Theta becomes
: positive.
: i think sometimes ppl are also interested in the so-called
: "driftless theta" by ignoring the discount
|
