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期权希腊参数是什么?

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不同的模型如何影响期权希腊人?

对于 Delta,粗略地说,交易者倾向于从以下方面考虑:$$ \Delta = \frac<\partial C(S_0;K,T)> <\partial S_0>+ \left。\frac<\partial C(S_0;K,T)> <\partial \sigma(S_0;K,T)>\right\vert_> \frac<\partial \sigma(S_0; K,T)> <\partial S_0>$$ 其中我考虑了隐含波动率 $\sigma(S_0;K,T)$ 的欧式看涨期权 $C(S_0;K,T)$,但不失一般性。上述方程可以重新表示为: $$ \Delta 期权希腊参数是什么? = \Delta_ + \nu_ \frac<\partial \sigma(S_0;K,T)> <\partial S_0>$$ 其中RHS 中的第二项有时称为影子增量:它与隐含波动率(表面)预期如何随现货变动有关。市场经常表现出不同的这种波动机制,从业者提出了各种粘性假设或经验法则来捕捉这些,请参阅Emmanuel Derman的开创性论文。

事实证明,做出一个特定的建模假设(即为底层证券的动态选择某个数学模型),隐含地塑造了现货/隐含的波动率动态。例如,在 Black-Scholes 中,您显然是粘性打击,因为该模型理论上规定波动率 (= IV) 是恒定的: $$ \sigma(S_0+\Delta S_0;K,T) = \sigma(S_0;K, T) $$ 使得 $$\frac<\partial \sigma(S_0;K,T)> <\partial S_0>= 0$$ 和 $\Delta = \Delta_$。在更精细的扩散框架中,该术语不为零。通常,在股票市场(负偏斜,即 $\partial \sigma/ \partial K < 0$)中,您将拥有: $$\Delta_ \leq \Delta_ \leq \Delta_$$因为,在不均匀局部波动率模型 à la Dupire 您可以显示 $\frac<\partial \sigma(S_0;K,T)> <\partial S_0>< 0$(粘性隐含树/粘性局部增量)。另一方面,在空间同质随机波动率模型(例如 Heston)中,您有 $\frac<\partial \sigma(S_0;K,T)> <\partial S_0>= -\frac\frac <\partial \sigma(S_0;K,T)> <\partial K>> 0$(粘性货币)。

这可能会令人困惑的是,在给定的建模假设下,您可以设置数值方法来计算几乎任何类型的 Delta,即不一定是模型一致的 Delta(这在Lorenzo Bergomi的最新著作中得到了很好的解释) )。这可以通过查看计算 Delta 的简单碰撞和重估方法来理解,例如中心有限差分近似 $$ \Delta = \frac $$ 使用这种方法,您通常会获得不同的 Delta 值,具体取决于通用模型参数 $\theta$ 期权希腊参数是什么? 期权希腊参数是什么? 中的哪些变量随着定价函数 $V( S_0;\theta)$。例如,在 Black-Scholes 中,除了冲击 $S_0$ 外,您可以选择使隐含波动率 $\sigma$ 根据某个粘性假设(这与理论行为背道而驰)演变,或者您可以保持不变,这将与模型预测的一致。

最后,请注意 Vega 应该被理解为一个超模的希腊语。换句话说,Black-Scholes Vega 应该被视为对违反 BS 建模假设本身的敏感性。从这个意义上说,它可以与例如 Heston 中 Heston 参数的敏感性进行比较。话虽如此,如果您想要对完整 IV 表面(这是 BS Vega 在数学上表示的)的平行位移的灵敏度,仍然可以在 Heston 和其他模型中获得它,但这很少可以通过分析来完成。它通常需要某种形式的冲击 IV 表面(!套利机会)+ 重新校准模型方法。

期权希腊参数是什么?

公式和技术细节

希腊字母的解析解

二叉树计算得到希腊字母

重新回顾通过Rubinstein二叉树的方法计算金融工具。对于给定的时间长度,例如,期权的到期期限,时间跨度被步长等分成相同的大小。每期,被称为时间步,与价格情景相联系,称为时间节点。每个时间节点都有两个分支,一个分支向上,一个分支向下。 期初,标的资产价格 ,在下一步,价格会上涨到 , 这里 , 或者下跌到 。

将 表示为标的资产的即期价格, 是期权的公允价值。所以,可以估计期权的delta为:

这里 是期权价值的变化量, 是标的资产的价格变化量了 。在二叉树中,让 和 分别表示为 和 的期权价格。这里期权的delta可以通过下面的函数计算得到:

Gamma可以通过delta变化与标的资产价格变化之比得到。计算gamma,在第2步节点处的期权价格是需要计算得到的。假设第2步的公允价值为 相应可能的标的资产价格为 ,注意,这里 。为了估计gamma,这里两个delta可以通过下面公式计算得到:

期权希腊参数是什么?

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Short naked options are calls or puts that are sold that have nothing to limit their risk (shares of stock, long options).

期权交易中有一些参数或者叫指标它们使用希腊字母来表示的,所以我们称他们为希腊值。最主要的希腊值有四种,他们分别为Delta, Theta, Vega, Gamma。希腊值在期权交易中是一个非常抽象的概念,但是掌握希腊值会对我们交易期权提供巨大的帮助。在这次节目中我们要来谈一下希腊值的重要性以及几种希腊值的由来。

The Greeks are a set of risk measures named after Greek letters. Greeks are abstract concepts, sometimes confusing. But understanding them can significantly improve our trading skills. The most basic yet important ones are Delta, Theta, Vega, and Gamma. In this episode, we discuss the importance of using Greeks and where they come 期权希腊参数是什么? from.

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