# Is there an academic framework for deciding when to sell in-the-money call options?

I've been buying 1-year at-the-money call options on various stocks as a way to increase my leverage.

I almost never regret selling them once they are up 40%.

There are many times when they've been up 20% and I didn't sell but later wished I had.

I'm interested in gaining a better intuitive understanding of the tradeoffs I am making here. It seems to me that by doubling my price target I am more than doubling the variance in my outcomes. I think I'm being too greedy and need to dial it back.

In short, when should I sell in-the-money options?

If any academic framework worked, your teachers would be the richest people on the planet. However, you must read up on macro and micro economic factors and make an educated guess where the market(or stock) would be at the date of expiry. Subtract the Strike Price from your determined price and calculate your potential profit. Then, if you are getting paid more or less the same thing as of today, sell it and switch to a safer investment till expiry (For example:- Your potential profit was \$10, but you are getting \$9 as of today, you can sell it and earn interest(Safer investment) for the remaining time.)

Its just like buying and selling stocks. You must set a target and must have a stop loss. Sell when you reach that target, and exit if you hit the stop loss. If you have none of these, you will always be confused(Personal experience).

• Probably the stop loss/target exit price should be proportional to the amount of time left on the option and the historical volatility of the underlying. – John Shedletsky Jun 2 '15 at 22:35
• Which is basically what you said. – John Shedletsky Jun 2 '15 at 22:41

based on my understanding of your query...well you need to understand ATM and ITM options. The delta and gamma factor specifically. Usually delta of ATM is around 0.5 while ITM option is above than that say 0.6 or 0.8 or 0.9 and deep ITM is very close to 1. for every movement of 1 buck the ITM will move say 1.6, ATM 0.5 and OTM 0.3 approx

Say a ABC stock price is Rs. 300 so if you check option chart you try to see which one is closer. Suppose you find strikeprice of 320 / 300 / 280. So 320 is ITM, 300 is ATM and 280 is OTM for call options. So will the delta value (e.g 0.66 / 0.55 / 0.35). So suppose if stock price rise by 7% i.e Rs. 321 then strikeprice will rise simultaneously. Say ATM CE300 is rs.10 it will start rising by 0.55 i.e. Rs.10.55. The moment the share price move from Rs.300 to Rs.320 your ATM will turn to ITM.

Now the tricker part if you buy OTM and the share price rise by 15% your OTM will now become ITM and your profit will roll around 100% to 120% approx.

The Captain Obvious answer is that you should sell your ITM option at their peak price before they start to decline in value.

Now we both know that is unknowable so we have to try Plan B, C through ?

When your outlook for the underlying changes, sell the call.

Like most of us, if you're not Carnak The Magnificent and you have no idea when the stock will correct then use trailing stops.

One year options have low theta decay which increases as time passes. A loose rule of thumb for ATM options is that the rate of time decay is approximately the square root of the time remaining. As an example, a 9 month option will lose 1/3 of its value in 5 months then another 1/3 of its value in the next 3 months and the last 1/3 of its value in the last month. So roll out or close your long calls as the rate of decay increases.

If call value has increased, consider reducing risk by rolling your call up a strike or more. You'll be giving up some of the upside potential since the new call will have a lower delta but your cash at risk will now be lower.

Consider converting to an more limited growth + income position by selling short term OTM calls against your ITM long call (diagonal spread). Upside reduced but cost basis lowered.

There's no one size fits all answer. You have to use good judgement with these decisions.

Good judgement comes from experience. Experience comes from bad judgement.

You can benefit from trades when there are differences in either knowledge or preferences between you and other participants in the market. If you have special knowledge, then you should use that knowledge to figure out when to exit, rather than asking the general public, who has access to the same knowledge as the market. If you have different preferences, then we would have to know what those are to decide what maximizes your utility.

The more ITM a call option is, the more it acts like the underlying stock. So if you prefer options to stocks, you should prefer ATM options to ITM options. So if you have a consistent utility function, and benefit more from call options than stocks, you probably would benefit from selling any ITM options you have and using the money to buy ATM options. But it's likely that you don't have a consistent utility function, and are basing your trades on irrational motives.