Chooser Options. A chooser option is a derivative that allows its holder to decide at a predetermined time before expiry whether the derivative will be a European call or put option that is, whether the payoff at maturity will be that of a call or put option). Consider a stock that is worth 100 today. Over each month its value either grows by a factor 1.1 (with probability p = 0.7) or decreases by a factor 0.9 (with probability 1-p=0.3). Assume also that the monthly interest rate is constant at 5%. Determine the arbitrage-free price of a European call option on the above stock with strike price 100 and expiry date in three months. Determine the arbitrage-free price of a European put option on the above stock with strike price 100 and expiry date in three months. Consider a chooser option on the above stock with strike price K= 100 and expiry date in three months. At the end of the second month from now, the holder may decide whether the option is a European call or put option. Calculate the arbitrage-free price of this chooser option. Determine a dynamic (state and time dependent) portfolio of the underlying stock and the risk-free instrument that replicates the price of the chooser option over the first two months