Let’s say I know that the probability of a merger-acquisition happening is p=1/4, the payoff i’d get in 6M (the time of the merger announcement) is 30. If the merger fails (q=1-p=3/4), my payoff is -10. What is the price of the call? And what are the risks involved and hedge?
Your product is not a call, whose payoff would be of the form $Max(S-K,0)$, it is more like a binary option.
If your stated probabilities are (somehow) risk-neutral, then the price is simply the (discounted) expected value.
If -more likely- these are just subjective probabilities, and you cannot trade the underlying risk factor to hedge, then there is no unique price for this asset and your risk preferences need to enter the equation.