Rman,
Please forgive the rambling giberish. I should have immediately defined my terms. Better late than never, as the saying goes...
Options and warrants (derivative instruments, generally) lend themselves to rigorous mathematical analysis. Certain properties of these instruments, by convention, have been assigned Greek letter names. The most important of these "Greeks" is "delta." Intuitively, "delta" refers to the degree that a particular option's fair value will shadow price movements of the underlying security. The mathematical representation of "delta" is the first derivative of the option's fair value, with respect to the market price of the underlying. (That is what my "slope" reference was all about.)
If it has been a while since you cracked open a calculus text, don't worry. Following are a few rules of thumb and examples which should be sufficient to illustrate the point (assume that the options in these examples are calls, not puts):
1. Deep in-the-money options will have "deltas" very close to 1.0. That means that, for every 1/8 that the underlying appreciates (or loses) the option will also appreciate (lose) 1/8. Note that, after several consecutive losses of 1/8, the option may no longer be quite so deep in-the-money. Thus the "delta" would change (become lower) as the price of the underlying approached the option's strike price.
2. At-the-money options will usually have "deltas" of approximately 0.5. That means that, should the underlying appreciate (lose) 1/8, the option will appreciate (lose) 1/16.
3. Let's assume that LGNDW has a current "delta" of 0.875. Let's further assume that LGND's bid opens up 1/4 tomorrow morning. Theoretically, LGNDW's bid should rise 7/32 (= 0.875 * 1/4.) However, should LGND instead open down 3 points, the fair value of the warrants would *not* decline by 2.625 (= 0.875 * 3,) because 3 points is too great a range for the "delta" to remain constant. In the latter case, the warrants would lose somewhat less than 2.625.
Congratulations on those rockets you flew today,
RB
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