3. (30 pts) A chooser option is an option, which gives the option buyer a fixed period to decide whether the derivative will be a European call or put option. In particular, consider a binomial tree with So 100, u = 120%, d 80% and r = 10%. Suppose a chooser option with strike price K = 105 has a specified decision time n=2, when the buyer has to decide whether this derivative will be a European call or put option. At the expiration time N = 3 the option expires. If the buyer has chosen that it is a call option, then the payoff at time 3 is (S3 K)+; otherwise, if the buyer has chosen that it is a put option, then the payoff at time 3 is (K S3)+; (a) Determine the buyer's decision at time n = 2. (Hint: the decision depends on w1w2, and the buyer chooses the option which has higher price at time n=2.) (b) Calculate Vo, the price of this chooser option at time 0. (c) Consider a European call option with the same strike price K 105, and expiration time 3. Price this call option at time 0, i.e., calculate V.. (d) Consider a European put option with the strike price and expiration time 2. Price this put option at time 0, i.e., calculate V. (e) Compare Vo with VC + V!. K 1+ri 3. (30 pts) A chooser option is an option, which gives the option buyer a fixed period to decide whether the derivative will be a European call or put option. In particular, consider a binomial tree with So 100, u = 120%, d 80% and r = 10%. Suppose a chooser option with strike price K = 105 has a specified decision time n=2, when the buyer has to decide whether this derivative will be a European call or put option. At the expiration time N = 3 the option expires. If the buyer has chosen that it is a call option, then the payoff at time 3 is (S3 K)+; otherwise, if the buyer has chosen that it is a put option, then the payoff at time 3 is (K S3)+; (a) Determine the buyer's decision at time n = 2. (Hint: the decision depends on w1w2, and the buyer chooses the option which has higher price at time n=2.) (b) Calculate Vo, the price of this chooser option at time 0. (c) Consider a European call option with the same strike price K 105, and expiration time 3. Price this call option at time 0, i.e., calculate V.. (d) Consider a European put option with the strike price and expiration time 2. Price this put option at time 0, i.e., calculate V. (e) Compare Vo with VC + V!. K 1+ri