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I have been trying to understand options and how to choose Strike prices and Expiration dates as well as the greeks, but I'm not sure I get it. I've ignored volatility or vega for now.

From what I've read it seems the more OTM your strike price the cheaper it is. If correct this leads to more profit. The downside is your break-even is harder to achieve and your risk of total loss is higher. Another way to think about it is that your OTM will make you more profit if you are right because when the stock goes the way you forecasted your delta increases and your call/put price was much lower than an ITM would have been. If XYZ is at 100 you can buy a call at 110 (OTM) or 90 (ITM). In both cases, if the stock moves to 120 you will profit, but the OTM will be more so due to lower cost. The ITM may profit less but could also profit at lower increases like 105 and if the stock doesn't move or goes down you would lose much less with the ITM.

Shorter expirations dates are cheaper. They also have a higher risk as you have less time for the stock to go the way you forecasted and theta will increase at a faster rate.

If you think a stock is going to go up then the most profitable (riskiest) strategy would be a Short expiry OTM. XYZ is 100, you buy a 110 call with a one-week expiry. If XYZ goes to 110 in a day you can sell for a large profit as you delta increased and your call price was very low. You could also have used a three-month expiry. After day 1 you could still sell for a profit but it would be less because the longer expiration costs more. Or you could hold on if you expect the stock to increase further as you don't have to worry about theta as much, although this could risk the stock price changing direction and losing your profit.

Alternatively, if you weren't as confident in your forecast or are more risk-averse you could buy a 90 call. If the stock goes to 110 you still make a profit, but less so because the ITM costs more. It would also be safest to choose a long expiration as you have more time for the stock to increase and less theta.

ITM long expiry is the least risk/reward and OTM short expiry is the most risk/reward? And this is why OTM short expiry is so much cheaper.

Is this all correct so far? Some things seem counter-intuitive. I read that delta increases if you're in the money the closer to expiration you are. So using the above example if you had an OTM 110 call with one-week expiry and XYZ moved from 100 to 110 in day 1, assuming the stock doesn't change after day 1 is it best to sell on day 1 to min theta or should you wait until day 7 to max delta? I think day 1, but there may be an optimal point in-between. I tried to read about gamma theta tradeoff but just got confused.

I have tried to use an options calculator to visualise results but some are confusing me:

https://www.optionsprofitcalculator.com/calculator/long-put.html

Using the above I put in spy at current price 100 and then did an OTM Put 95 and an ITM Put 105 both expiring in June. The profit loss curve was higher for the ITM at all dates. If I divide the profit by cost to get a profit ratio the ITM is still more profitable until the current price reaches roughly 70 which seems way off. Am I missing something or using this tool wrong?

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