wichever let you buy more delta given you sum of money, remember the near in the money options will not colapse like the out the money calls
If you are planning to hold for 1-3 days then back month options are not the best choice as they are slower to respond. How about short term OTM!? ATM would give you a good bang for the buck.
I have a similar question. Assume no change in IV. If I expect an "X" pt move, I can calculate what the options will be worth "Y" days from now. Based on an equi-dollar investment (spec ?), I can then determine which strike will give me more bang for the buck. I could also look at an option chain and extrapolate from it what the option prices would be for a change in price only. Obviously, price moves in strike price increments would be just a quick visual. Is there a down and dirt quick way to use delta(or some other Greek) to guesstimate this and pick the strike? If this isn't clear, I'll provide an example.
X multiplied by Delta gives you an option's move (roughly, cause you don't account for Gamma, Theta and Vega). You can also take a $ amount and then see how many contracts that buys you for different strikes. Then multiply that by delta to get the total deltas for each strike, then compare. But don't forget about Time Decay!
Buying calls into a market dip with it's corresponding IV ramp is a crap trade. As the market recovers vols get's crushed. Just look at how poorly calls performed (relative to the steepness of the move) off the August lows.
I decided to run the scenario through my software to see what it says would be the best call options to purchase f you expect a relatively big move up in the next 3 days. I chose to run it on the options of the SPY (currently at $150.15). For my target I said that it would go up between 2.5% and 5% (between 154 and 157.75) by October 30th (3 trading days from now). I also said to pick the best trade you can with $2,400 of capital (I chose that amount because you would need about that much to purchase just one December '09 150 (the ATM) call). I also told it i would not buy any options with an Asked price of less than 35 cents). The results with the top 15 trade recommendations ranked by expected return are attached (note the third-to-the-last column which is labeled e.r., for expected return, based on your target projection coming to pass). As you might expect for such a short-term trade, the top recommendations are all in the front month. Notice also that the top recommendation is the farthest OTM call in November costing 35 cents, and then simply goes down progressively by strike until you hit the ATM strike, when it then switches to the 2nd month out. Using the same amount of capital for each trade allows you to easily make a direct comparison between each. Notice also the last column, p.p., which stands for probability of profit. The expected return may be larger if your prediction comes to pass, but statistically the probabilities are against you when you buy far OTM.
I thought it might also be helpful to look at a Matrix of all the call option on the SPY showing their Deltas. It may seem that the trade recommendations posted previously are done just by picking the smallest deltas in the month with the least time left. That is why i also added one additional column after Delta, which is labeled %Double. This number is a measure of leverage, and it tells you what percentage the underlying has to move for the option to double in price. Note that for such as short term trade, with a relatively large move projected, the highest expected return if the options with the smallest %Double, and the trade recommendations are really just recommending that you buy as many options with the highest leverage you can with the capital provided.
I admire your effort but your results are quite skewed from reality. You are suggesting an 70point move in SPX which will take vix down to below 16. That vol crush will significantly hurt your OTM front months.