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A CD issued by Bank XYZ will pay 100% (Hereafter referred to the “participation rate”) of increase in S&P 500 (excluding dividends) at a 5.5-year horizon, if that return is positive and zero interest otherwise. The CD guarantees at least repayment of the principal. The S&P 500 index is now 1000. Each CD has a face value of $1000. Suppose that at the time the CD was issued, the risk-free rate was 6%, the dividend yield on the S&P was d = 1.5%, and the volatility of the S&P index was 25%. Your analyst tells you that a European call of the S&P 500 index, at-the-money, for 5.5 years, is valued at $306 according to the Black&Sholes model, with its delta equal to 0.70. However, such a long term call is not available on major option exchanges.

Please analyze if Bank XYZ can make a guaranteed profit from issuing such a CD provided above information. If Bank XYZ wants to hedge its risk associated with issuing the equity linked CD, how should it do so? What is the maximum participation rate Bank XYZ can provide to break even in issuing this CD?
应用：与股票挂钩的CD
银行XYZ发行5.5年期100%（此后成为“参与率”）支付SP500的增长（不包括红利），前提是回报为正或者零。CD本金保付。SP500指数现在是1000，每一份CD的 面值是$1000。假设CD现在发行，无风险收益率是6%，d=1.5%，SP指数的波动率是25%。你的分析师告诉你根据BS公式计算出在价的欧式买权价格是$306,delta=0.70.然而，如此长的的买权在主要的期权交易所没有交易。
请分析如果XYZ银行根据以上的信息是否可以通过发行这样的CD获利。如果银行XYZ想要对冲此与CD挂钩的风险，它将如何操作？银行XYZ发行此CD如想盈亏平衡最大的参与率是多少？

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