Iâm struggling for a while now with a question about options, namely ‘which is the best option to buy?’. I have various books on options, but Iâm not an mathematician and donât have (yet) any extensive hands-on experience with options.
According to Cohen (Options Made Easy, 2nd Edition), the Delta of an option is the âchange in option price relative to the change in underlying asset priceâ. He goes on to give an example of an option with an Delta of 0.5 which moves $1, in which case the premium of the option will increase with 0.50 (call) or decrease with 0.50 (put).
Even though Deltaâs of options are changing with each change to the various components which make up an option premium, Iâm wondering if a Delta can be used to determine the premium of an option given a certain target.
For example, letâs say stock XYZ trades at 50 dollar and we have an price target of +10% (so the share price of XYZ increases to 55 dollar; +$5). Letâs say an optionâs current premium is 2.00, with an Delta of 0.40. Can the option premium at the target of 55 dollar be calculated with the following formula?
Current option premium + ( (share price target - current share price)
* current delta of the option) = Approximated option premium at the price target
So, with the example figures this option will be worth..
2.00 + ( (55 â 50) * 0.20) = 3.00
â¦at the price target?
Besides this, Iâm wondering:
- Isnât the gamma (that is, the change
in delta relative to the change in de
underlying asset) needed for such an
- If we have a time period
in which to achieve this price target
of $55, can the Theta (time decay) be
incorporated in the calculation of
the approximate value at the price
- And, above all, requires this
really so much calculation or can the
approximated value be more easily and
better be derived from something
else? (like, say, the same strike of
the option at and different
expiration month, correcting for time
My original angle to my question was more in wondering if there was a sort of ârule of thumbâ which an investor could use, in trying to choose between different strike of options. The underlying idea to my question was that, if somehow the option premiums could be guessed given the target for the stock, then the investor would be able to select the âbestâ option for his outlook (i.e. the one with the highest potential return). With the same ârule of thumbâ an investor could calculated the potential downside, given his stoploss on the stock.
I agree with DumbCoder that an option model (like the Black and Scholes model; see https://secure.wikimedia.org/wikipedia/en/wiki/Black%E2%80%93Scholes#Mathematical_model) has the potential to answer this question, even though I don’t (yet) understand this model.
Any more insights would be highly welcomed,