老师您好，这个图的横坐标是外汇汇率吗？为什么当外汇汇率分布呈现肥尾时就会产生波动率微笑啊？波动率微笑的图横坐标是执行价格k啊，两张图如何联系起来？

老师index的variance为什么比components的variance上升的更快，常理讲大盘的波动率应该没有个股的波动率大啊，我带了个数算了下 也行不通啊

期权映射模型为什么只考虑行权的情况，没有考虑不行权的情况呢？

老师信用风险122页这一段Another difficulty with the Merton model is that default is too ​predictable. Remember that to obtain prices of debt in that ​model, we make the Black Scholes assumptions. We know that ​with these assumptions firm value cannot jump. As a result, ​default cannot occur unless firm value is infinitesimally close to ​the point where default occurs. In the real world, default is often ​more surprising. For instance, a run on a bank could make its ​equity worthless even though before the run its equity value was ​not close to zero.没太看懂能讲一下吗？谢谢

老师您好，quanto option的underlying到底是什么？按照讲义上写的截图一quanto call on Nekkei，那么underlying是Nekkei，但是这样的话截图二我就不理解了，它说当increasing Nekkei，this is favorable for the call seller，我觉得Nekkei作为underlying，当其指数上升时，应该对call buyer有利啊？

如果信用风险中不关注cash flow 是否容易引发流动性风险，不是也间接影响到违约吗

老师，我蒙了，为啥有时候需要除以根号12，有时候不用？哭哭

老师书上第121页，One way ​Panel B ​Debt value ​.... 42 ​40 ​10 ​Maturity ​-I ​0.2 ​is to compute the delta-VaR by transforming the risky ​debt into a portfolio of the risk-free bond and of the ​debtor's equity if we are computing a VaR for a short ​period of time. A second way is to compute the Monte ​Carlo VaR by simulating equity returns and valuing ​0.1 ​Interest rate ​volatility ​the debt for these equity returns. If the firm has other ​assets, we must consider the correlations among the ​asset returns.这段说计算var 其中一种把deltavar 看作无风险债务和债权人的权益来计算，第二种通过模拟股票回报率来计算，就没看懂，能解释一下吗

没太懂为什么可以用画倒三角的方法判断肥尾还是痩尾。这里为什么一个正态分布可以用倒三角来表示呢？它的横纵坐标又是什么？

老师您好，请问这道题为什么不需要把年波动率除以根号12，得到月波动率？