A bank is offering a 10 year equity linked CD that pays the investor their principal back plus some % (the participation rate) of the appreciation in the S&P Index. Assume that the principal value of the CD (initial proceeds from the investor) is $1,000 and that the current level of the S&P Index is $1,000. A 10 year call option on the Index with a strike rate of $1,000 is $487.8438. In offering this product the bank is required by its regulator to dedicate/invest $200 of its own money/Capital alongside this product to cover any risk blowups. The bank requires a 20% annual ROE on its Capital which will be cumulatively payable in year 10. It can invest any fixed income proceeds in 0 coupon bonds that earn an annual rate of 10%. Use continuous compounding.

a) What should the participation rate on this equity linked CD be so that the bank exactly meets its ROE requirements?

b) If the index volatility increases before the call is purchased what will happen to the participation rate on the product, will it be increased or reduced? Briefly outline your conclusion.