Seems like that 3rd term is gamma, correct? If so, then I guess I would think of it as adjusting the delta for how deep in/out of the money the option is?
I'm pretty fried at this point, but that's what I'm going with.
... which basically says, the option's duration is the
(1) duration of the underlying instrument (futures) times
(2) the option's delta, times
(3) the ratio of the underlying price to option price.
Here's my take:
(1) is very intuitive
(2) makes some sense (because option & futures prices wouldn't necessarily move in lock-step) (3) is puzzling? Why does duration move up with a higher ratio of the prices?
Book explanation is that (3) measures the leverage, and a higher price ratio means higher exposure to interest rate changes... if you think how an interest rate future's priced, it seems circular reasoning (higher interest rates means higher prices).
In my opinion, the last ratio shows how much more your option position will be sensitive to interest rate changes.. For example, if the underlying price is 200 and the option price is 20, option will be 10 times sensitive to interest rate changes than the underlying instrument because you will have to buy 10 options to make the dollar durations match..
I am not sure, though, that this intuition is correct..
I thought Gamma measures the relationship between option delta and underlying price..
发表于 2011-7-13 13:03
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