You are attempting to value a call option with an exercise price of $$105$ and one year to expiration. The underlying stock pays no dividends, its current price is $$105,$ and you believe it has a $50\%$ chance of increasing to $$120$ and a $50\%$ chance of decreasing to $$90.$ The risk$-$free rate of interest is $10\%.$ Consider one share of stock and two written calls. Calculate the call option's value using the two$-$state stock price model.