隐含波动率

波动率是B-S公式中唯一不能直接观察到的变量，一般通过历史波动率或隐含波动率求取。

Volatility of B-S formula can not be directly observed , through the general history of volatility or implied volatility strike .

最后，本文用数值分析比较四个模型对VIX隐含波动率曲面的拟合效果。

At last , numerical analysis in this thesis compares the four models in fitting VIX implied volatility surface .

其次，通过对比RBF网络模型与B-S模型、BP模型，发现不论是使用历史波动率还是隐含波动率，RBF网络模型都要优于B-S模型、BP模型。

Secondly , comparing RBF network models and B-S model , BP model , no matter using historical volatility or implied volatility , RBF network models are superior to B-S model and BP model .

首先，因为存在衍生品隐含波动率与远期LIBOR波动率之间的封闭解关系，避免了复杂的数值校准过程，这使得市场模型的校准过程相当容易。

First of all , the relationship between implied volatility and forward LIBOR volatility can be represented by a closed-form solution , which avoids the complex numerical calibration process .

首先，我们采用ME、MSE、MAE和MRE四种误差指标对分别使用历史波动率和隐含波动率的基于四种RBF网络算法的定价模型进行评价。

Firstly , we use ME , MSE , MAE and MRE to evaluate the pricing models based on four RBF network algorithms which use historical volatility and implied volatility .

通过算法参数和仿真结果的比较发现，利用隐含波动率的RBF网络模型要优于利用历史波动率的RBF网络模型，且前者所选取的神经元个数要多于后者所选取的。

By comparison of algorithm parameters and simulation results , we find that the RBF neural network model with implied volatility is superior to the RBF neural network model with historical volatility . The number of neurons of the latter is less than the former .

在定价过程，同时对历史波动率、隐含波动率、GARCH（1,1）模型下的波动率三种波动率进行了区分，并分别应用于定价模型中比较定价结果。

When we use the three models to price them , we also distinguish volatility as history volatility , implied volatility and volatility in GARCH ( 1,1 ), and use all of them in each pricing model for comparison .

回报的偏峰现象和隐含波动率的微笑现象是Black-Scholes模型无法解释的两个现象，本文引入了双曲波动率模型，并研究了在这一模型下的障碍期权的定价问题。

The phenomenon of return kurtosis and volatility smile is contradict with the Black-Scholes model . We introduce the hyperbolic volatility model to overcome the drawbacks , and we conduct research on barrier option pricing with this model .

基于香港市场的隐含波动率动态模型研究

Research of Dynamic Implied Volatility Models Based on Hong Kong Market

这是因为隐含波动率通常高于实际波动率。

This is because implied volatility is generally higher than realised .

期权隐含波动率微笑成因分析

An Analysis of the Determinants of Implied Volatility Smile on Stock Option

隐含波动率的建模、计算方法及其应用

Modeling , Computing Methods of Implied Volatility and Its Application

本研究是由二篇有关于个股选择权隐含波动率之文章所构成。

This study contains two essays in implied volatility of individual stock options .

无模型隐含波动率及其所包含的信息研究

The Model-Free Implied Volatility and Its Information Content

由期权平均价格确定隐含波动率的最优化方法

The Optimization Approach for the Determination of the Implied Volatility through the Average Option Price

资产收益分布可能具有非对称、尖峰厚尾特征以及隐含波动率微笑。

The asset returns may represent non-asymmetric leptokurtic features and " implied volatility smile " .

确定原生资产的隐含波动率无论是在理论还是实际应用上都有重要意义。

Identifying the implied volatility of underlying assets is very important for both theoretical and practical applications .

因此投资者完全不必如此自满地任由隐含波动率游离于如此低位状态。

So it need not necessarily be that investors are complacent in allowing implied volatility to drift so low .

首先，对波动率的微笑和期限结构进行了详细评述，并通过波动率的指数矩阵计算了隐含波动率。

Volatility smiles and term structure are calculated through index matrix of volatility in the fourth chapter detailed introduction .

实证结果显示套利风险的确会影响到个股选择权的隐含波动率曲线。

The empirical results reveal that arbitrage risk does affect the slope of the implied volatility curve for stock options .

出乎意外地的是，皮质醇上涨与用来测量预期将来资产价格变动的隐含波动率呈正相关。

Remarkably , cortisol increased in direct correlation to implied volatility , a measure of expected future variance in asset prices .

第一篇文章所研究的是关于套利风险对于个股选择权之隐含波动率曲线斜率的影响。

The first essay examines the effect of arbitrage risk on the slope of implied volatility curve for individual stock options .

如果套利风险会影响隐含波动率曲线的斜率，则个股选择权与套利风险之间是有关连的。

If arbitrage risk affects the slope of implied volatility curve , then there is a connection between stock options and arbitrage risk .

通常金融界采用平价期权的隐含波动率作为实际波动率，但这与市场的实际情况有较大偏差。

The finance circles usually use implied volatilities of the at-the-time options as the real ones which has a big deviation with the reality .

此外，投资人所抱持的信念差异也与套利风险有关。第二篇文章的研究重点在于选择权隐含波动率曲线不同模型之间的比较。

By investigating the slopes for OTM puts and OTM calls , some effects of the arbitrage risk on the implied volatility curve are asymmetric .

由于两平期权具有较高的流动性以及其隐含波动率对价格误差具有较低的敏感性，因此两平期权的隐含波动率通常被人们认为是未来波动率的较好预测。

Due to the high liquidity of at-the-money option and the low sensitivity of its implied volatility to the price error , the at-the-money implied volatility is often considered a good measure of future volatility .

显然，这与实际情形是存在巨大差异的，这种不一致主要表现在，实际观测得到的金融市场衍生证券的价格的隐含波动率存在波动率微笑的现象。

Clearly , this and the actual situation is a great difference , this inconsistency is mainly manifested in the observed derivative securities by financial markets implied volatility of prices exist " volatility smile " phenomenon .

对于早已大跌的投资品种（比如黄金、美国国债、新兴市场等等），隐含波动率凸性概念6个月来已显而易见。

In terms of implied volatility in everything that was already crashing ( gold , Treasuries , emerging markets , etc ) , that concept has been pretty straightforward for going on for six months now .

此外，本章还介绍了权证波动率的估计方法，包括历史波动率、隐含波动率和已实现波动率。

S model can be used to solve the whole warrants pricing of the SSE & SZSE ; More ever , this chapter also gives an introduction of the estimation methods of volatility , including historical volatility , implied volatility and realized volatility .

外汇隐含波动和波动率指数在继续增加。

Volatility continues to increase both in FX implied vols and VIX index .