I created a P/L graph for 2 CALL OPTION contracts XYZ Jan 15 2021 120 Call. I want to take some profit before the expiration of January 15, 2021. What technical data that I can use to figure out a reasonable price for which the CALL OPTIONS can be sold? There should be some historical data after I bought to increase the probability of a certain price a stock can hit before it can drop. Also any data that I can analyze after I bought the options to choose LIMIT, STOP LIMIT, TRAILING STOP MARKET or TRAILING STOP LIMIT.

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    There is no such thing as technical data which will tell you what an option WILL be worth in the future. You can project what it may be worth if you define how much the stock will move in what time period and what the implied volatility will be on that future date. The best that you can do is set a target price and continuously evaluate the situation going forward. There are option adjustments that can be made if the stock rises but I'll pass on speculating about that since your position didn't have all of the details (current stock price, premium paid). Dec 9, 2019 at 14:22

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You can certainly try to estimate the fair value of the option now, using the historical observed volatility as an estimate of the expected delivered volatility, the underlying, the time left and interest rates. You can compare that valuation estimate to the current market price and then decide what to do now. You can keep repeating that process until expiry.

However, if you want to try to forecast what the market's expectation of volatility and underlying price will be (and therefore what the market will pay for your option in the future), that is much, much harder. Most professional investors I know think that technical indicators are basically garbage. Good luck!

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