A bank is offering a 10 year equity linked CD that pays the investor their principal back plus some %(participation rate) of the appreciation in the S&P500 index. Assume that the principal value of the CD is 1000$ and that the current level of the SP500 index is1000$. A 10 year call option on the index with a strike rate of 1000$ 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 it 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.

1) what should be the participation rate on this equity liked CD be so that the bank exactly meets its ROE requirement?

2)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