A call option price is 1.6 and B call option price is 1.0. Both A and B are different products and A price is only avail on 1600 and B price is only avail on 1800. Long 100 contracts of A and short 100 contracts of B at 1.6 and 1.0 repsectively. The ratio is 1.6. THe problem : How to maintain the ratio of 1.6 the next day when prices move? A price is avail before B and say A price fall and you choose to long more but you don't know B price which is 2hrs less on 1600. Say you long addition 1000 dollar for A. When B price on 1800 short 100 dollar for B would not make the ratio equal to 1.6. Using different dollar would make the ratio equal but the dollar exposure would be different. Anyone?
Without getting into the details or the assumptions (which are not clear to me), but just on the strike availability aspect, you can probably get fills at any strike you want if you put in a limit order at an appropriate price (use a model or adjust from the prior close), even though no bid or ask is quoted initially. Usually someone will see your order and quote against it. Also you can look into maintaining delta neutrality of the overall position if you expect the two to remain closely aligned.
Limit order would not get the ratio price but the individual option price You may put a 1.6 limit order on A and get the price 1.6 but B price is unknown till 2hrs more. With B price fill at 0.5 you would get the ratio price of 3.2 which is higher than what you want. You may also put a limit price at 1 for B but B may not trading to 1 if B price is very low. Consequently you have to get what B price give on the close if didn't trade to 1 limit price to maintain delta neutrality and the ratio price you want 1.6 would be not 1.6 but some other price. The problem is due to B price is 2 hrs unknown at A
It is hard to comment further without knowing exactly what A and B are. Maybe you are talking about the same company's stocks traded on different exchanges in different time zones?
I suppose you can put on a synthetic long position (e.g. long call short put) on one exchange and a synthetic short position (e.g. short call long put) on the other. The strikes do not have to be the same.
There would be no simple ratio because the deltas of options at different strikes are different. That means that the values of the two strikes would move a different percent when the underlying value changes, destroying any ratio calculation.