老师您好，百题 金融市场与产品部分第6题，通过债券复制法为第二个债券定价，为什么债券1和债券3的份数之和要等于1？ 如果不等于1，比如价格为94.4的债券取1份，价格为101.30的债券取0.01529份，同样可以复制出第二个债券的现金流，这个组合的价格要比答案中X=0.52而Y=0.48的组合价格更便宜。这样做有什么问题?

delta是不是不管call还是put都是out of money时等于0，at the money等于0.5， in the money等于1？

80题EWMA模型里用ln(30.5/30)怎么理解?

An investor is long a long-term ATM put option on an underlying portfolio of equities with a notional value of USD 100,000. If the 95% VaR of the underlying portfolio is 10.4%, which of the following statements about the VaR of the option position is correct when secord-order terms are considered? C. The VaR of the option position is slightly less than USD 5,200. First-order term=5200可以计算得出，但是这里是long put,为什么后面的secord-order term是负的呢？如果这题改成short put, Gamma是负的，是不是就会slightly more than 5200?

A bank had entered in to a 3-year interest rate swap for a notional amount of USD 300 million, paying a fix rate of 7.5% per year and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded 1-yr and 2-yr annualized LIBOR rates were 7% per year and 8% per year, respectively. The value of the swap at that time was closest to which of the following choices? A. USD -14million B. USD -4 million C. USD 4 million D. USD 14 million 没有想明白老师上课说floating的价值是300million, 请老师总结下计算swap时候floating部分的计算方法，能结合图片更好，谢谢

什么时候需要把正态分布转化为标准正态分布求区间

老师，您好！ 第30题，为什么β会等于0.4936

老师想问两个问题：1.线性插值法就是指求平均数？若已知1年和4年的，求2年的，怎么求？ 2.题目如果给出semiannual，一般指coupon的付息和市场利率都是半年支付一次，但这道题说zero coupon，那payment是0。可市场利率折现还是按半年一次。是这么理解吗？

stack-and-roll中, 每次替换的也还是3个月的futures呀, 为什么说是longer-term?

老师，您好。 请问为什么计算σx 是除以n 而不是除以n-1