The current price of a non-dividend paying stock is $200 with a volatility of 30%. The risk-free rate is 6%. Consider a 1-year American put option on the stock with a strike price of $190. Assume that the option is optimally exercised. a) Use DerivaGem to create a 4-period binomial tree for this option. b) What is the probability that the option is exercised early? c) What is the probability that it is exercised at maturity? d) What is the probability that it matures out-of-the-money? The current price of a non-dividend paying stock is $200 with a volatility of 30%. The risk-free rate is 6%. Consider a 1-year American put option on the stock with a strike price of $190. Assume that the option is optimally exercised. a) Use DerivaGem to create a 4-period binomial tree for this option. b) What is the probability that the option is exercised early? c) What is the probability that it is exercised at maturity? d) What is the probability that it matures out-of-the-money