I’m 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 I’m not an mathematician and don’t have (yet) any extensive hands-on experience with options.
According to Cohen (Options Made Easy, 2nd Edition), the Delta of an option is the “change in option price relative to the change in underlying asset price”. 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 Delta’s of options are changing with each change to the various components which make up an option premium, I’m wondering if a Delta can be used to determine the premium of an option given a certain target.
For example, let’s 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). Let’s say an option’s 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 – 50) * 0.20) = 3.00
…at the price target?
Besides this, I’m wondering:
- Isn’t the gamma (that is, the change in delta relative to the change in de underlying asset) needed for such an calculation?
- 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 target?
- 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 value?)
Edit: My original angle to my question was more in wondering if there was a sort of ‘rule of thumb’ 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 ‘best’ option for his outlook (i.e. the one with the highest potential return). With the same ‘rule of thumb’ 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,