Howard Wolowitz works for Southbank Financial and he is calling you to offer what he promotes as a no brainer. During a phone call, Howard tells you that, upon investing AUD 10,000 today, you would be guaranteed not to lose money over the course of the next six months. Specifically, if the ASX200 index ends up lower in six months, you will get your AUD 10,000 back regardless; whereas, if the ASX200 gains value you will eam a return equal to 60% of the index return over the six months. To access this product Howard tells you that you will have to pay AUD 500 and adds it is such a great deal that I would sell it to my mother if she just listened to me!" Denote by So the current value of the ASX 200, by St the value in six months and by R the return on the index over the six months. a) Describe the payoff of the offered product as an option on the index. I.e., write the return received from the investment as a function of So and SI b) Assume index options are priced in the market according to the BSM model. You look up some information and find out that the risk-free rate in Australia is 5% per annum, the dividend yield on the ASX 200 is 2% per annum, and the volatility of the index is expected to be 25% per annum. Do you assess the product as a good deal? Why or why not? Please show all you workings