How to match future price from the market with the one computed with a model?

I have a future quoted in the market. Let's say $50 price. The price model of this future is : S * Exp (rate + storage - convenience - yield) How can I be sure that the model gives exactly the same price as the market ($50) and there is no arbitrage ?

If you don't, storage and convenience (like repo) are non-observable parameters which are plugs that make market price = model price, they are implied from the market price of the future. Thus by construction your model price should be equal to the market price.