The premium of the below call keeps falling although the price is increasing and it still has more than a month until expiry. The current spot price is 392.
Shouldn't the in the money strike premium increase?
I have attached the picture.
Options are generally viewed as having two types of value: "Intrinsic value" and "time value." The intrinsic value is based on the difference between the strike price on the option and the spot price of the underlying. The time value is based on the volatility of the underlying and the amount of time left until expiration. As the days pass toward expiration, the time value generally decreases, and the intrinsic value may move up or down depending on the spot price of the underlying. (In theory, time value could increase at some points if the volatility is also rising.)
In your case, it looks like the time value is decreasing faster than the intrinsic value is increasing. This may happen because the volatility is also going down (as suggested in the answer by CQM) or may just happen because the time to expiration is getting shorter at equal volatility.
As noted by DumbCoder in a comment to the original question, the Black-Scholes formula will give you more analytical insight into this if you're interested.
The answers and comment you received have clearly explained the meaning of intrinsic and extrinsic value as well as the relationship of time premium and implied volatility.
However, I think that there's a larger problem that hasn't been addressed. The current spot is 390 and the 390 call that you are looking at has no open interest, a closing price of 21.85 with a last trade of 22.80 (up 4.35%) and a current B/A of 24.40 x 26.65.
Based on that information, what's fair value for this option? A Black Scholes model will tell you that but from looking at sporadic trades under the above conditions, you can't tell at any given moment of time if the time premium is increasing or no unless you do a bit more analysis. To get an idea, you could average the B/A over a period of time and compare extrinsic.
There are a number of approaches to get a better idea. You could look at daily Implied Volatility sheets. Without access to that, you could compile it yourself from averaged IV numbers for the security and back it out via Black Scholes. Or for a visual, you could use the free IVolatility volatility charts (US stocks for me) that offers several vol graphs for optionable securities (3, 6 and 12 month looks at IV Index Call, IV Index Put, IV Index Call & Put, and IV Index Mean).