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How can you use binomial pricing model if you have three states (and one period)?

You wouldn't use put call parity, you would use the binomial option pricing model.

http://www.analystforum.com/article/frm/...

Let's say you sold an option on a stock that's currently worth $50. In the next period, it can either increase to $100, decrease to $25 or plummet to $10. (The probabilities being 50%, 49% and 1%, respectively). If the strike for the put is $15 and the put costs $1, what is the value of a call option? Is it possible to calculate this using the put-call parity?