是对 BS模型的隐含波动率与执行价格相关性的一个形容，主要是形容2阶微分 HEDGE的不完美性

转贴

Why there's a smile:

Imagine you buy an option with positive Vega Gamma (any OTM option, either high- or low-strike). You hedge the outright Vega by selling an ATM option (which has roughly zero Vega Gamma). Now you're got a parabolic payoff vs volatility, much like you did vs asset price in the Gamma example at the top. So, whichever way vol moves, you make money. Woo hoo! You're willing to pay up for that portfolio, above the standard zero-stochastic-vol (Black-Scholes) value. The more volatile vol is, the more you're willing to pay.

So this means that, if volatility is stochastic, you tend to be willing to pay more than the Black-Scholes value for OTM options, but not for ATM options (since they have no Vega Gamma). This means that implied volatilities will be higher for OTM options than ATM options, which is the smile.

是通过的OPTION和股票的不同组合来达到无风险组合的方法，一个是考虑到 2阶微分，另一个是考虑到3阶微分。

2阶微分，只能对小规模的变动起到 规避风险的作用（比如不管股票价格涨1分，还是跌1分，财富都不变）但是不能对大规模的变动祈祷规避的作用（比如股价变了1元），但是3阶微分就可以达到这个作用

这个是数学里的 泰勒级数 在OPTION里的应用

[此贴子已经被作者于2005-12-23 10:59:04编辑过]

大概了解了,另外这里的泰勒级数是用在随机积分的基础上的吧