All options in this question are of the European style, on the same stock that pays no dividend, and one option on one share of the stock. The stockis currently trading at $95. A European call maturing in 6 months with strike price equal to $100 is priced at $5. A European call maturing in 1 year with strike price equal to $105 is priced at $6. The risk-free interest rate is 10% with semi-annual compounding.

(i) Suppose Goldman Sachs has just sold a million chooser options to a hedge fund for $12 per option, or $12 million in total. Each chooser option has a strike price of $105, maturing in 1 year, and it gives the holder the right to choose at t = 0.5 years whether the option is a call or a put. What is the profit made by Goldman Sachs?

(ii) Describe in detail how GS can lock in the profit without running any market risk.