Suppose the risk$-$free interest rate is at zero per cent. A banker designs a new special bond for you that offers a $15\%$ annual coupon. You need to invest $$10000.$ The payoff of this bond one year from now depends on the value of GameFun Stock at that date. GameFun pays no dividends, has a volatility of $60\%,$ an expected return of $15\%$ and the current stock price is $$100.$

If the GameFun share price is greater than or equal to $$100$ one year from now, you will earn a coupon return of $15\%$ on your investment and, in addition, you receive back your initial investment of $$10000.$

If a GameFun share trades below $$100,$ you will receive $115$ GameFun shares.

a$.$ Find a portfolio of two standard securities that replicates the payoffs of this savings product. Be as precise as possible.

b$.$ Compute the NPV of purchasing the savings product. Is the offered coupon rate fair?

a should involve solving for delta and B