17. (Lecture Note 6) A Charlotte hedge fund is offering a new financial instrument called a happy call. It has a payoff at time equal to max(0.5, ), where is the price of the stock at time and is the exercise price. You always get something with a happy call. Let be the current price of the stock and let 1 and 2 be the current prices of European calls with exercise prices and 2, respectively. The current price of a European happy call is of the form: = + 1 + 2 Find the values for the constants , , and .

17. (Lecture Note 6) A Charlotte hedge fund is offering a new financial instrument called a "happy call". It has a payoff at time T equal to max(0.5ST, ST-X), where ST is the price of the stock at time T and X is the exercise price. You always get something with a happy call. Let St be the current price of the stock and let C and C be the current prices of European calls with exercise prices X and 2X, respectively. The current price of a European happy call is of the form: CH = St + BC + yC Find the values for the constants a, , and y. 17. (Lecture Note 6) A Charlotte hedge fund is offering a new financial instrument called a "happy call". It has a payoff at time T equal to max(0.5ST, ST-X), where ST is the price of the stock at time T and X is the exercise price. You always get something with a happy call. Let St be the current price of the stock and let C and C be the current prices of European calls with exercise prices X and 2X, respectively. The current price of a European happy call is of the form: CH = St + BC + yC Find the values for the constants a, , and y