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Option Greeks
Answers to Problems and Questions
1. Delta is the hedge ratio, a measure of option sensitivity, and sometimes
approximately the likelihood of the option ending in the money.
2. As time passes, the delta of an inthemoney option approaches one.
Call
option deltas are less than one, so an inthemoney call delta must rise with
the passage of time, everything else being equal.
3. With a striking price of zero, the call option would behave exactly like the
stock.
Its delta would therefore be 1.0.
4. Some strategies are constructed based upon a neutral outlook on the market.
If the position delta is not zero, then the position has an initial bullish or
bearish bias.
5. With European options, the sum of the call delta and the put delta is one.
This is approximately the case with American options.
As time passes, the
call delta will approach 0.5 and the put delta will approach –0.5.
The sum of
the two (the position delta) will not change, however.
6. In some circumstances delta is a useful measure of the approximate
likelihood that the underlying asset will finish inthemoney.
This means
that profit and loss diagrams can be annotated with the likelihood of reaching
various profit levels, especially those that are substantially in or outofthe
money.
7. Long options have negative deltas by convention simply because the time
remaining with a particular option can only decrease.
Time can pass, but you
cannot go back in time.
8. The lower the striking price, the higher the delta for a call option.
A bull
spread involves buying the low striking price (with a higher delta) and
writing the high striking price (with a lower delta).
This means the position
delta for a vertical bull spread will always be positive.
9. With little time remaining until expiration, the likelihood increases that an in
themoney option will remain inthemoney (and act like the stock), and
viceversa with an outofthemoney option.
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 Spring '10
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