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mx · 2022年05月10日

gamma和theta的计算没有看懂

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021205000046

问题如下：

Use the binomial tree in Figure 14.7 of Chapter 14 to estimate the delta, gamma, and theta of the option

选项：

解释：

The delta estimate is

202.098  −  38.8122,657.878  −  2,351.500\frac{202.098\;-\;38.812}{2,657.878\;-\;2,351.500}=0.5330

For gamma, we calculate two deltas from the nodes at the end of the second time step. The delta from the upper nodes, where the average index is 2,662.863, is

328.791  −  78.2792,825.726  −  2,500\frac{328.791\;-\;78.279}{2,825.726\;-\;2,500}= 0.7691

The delta calculated from the lower two nodes, where the average index is 2,355.911, is

78.279  −  02,500  −  2,211.821\frac{78.279\;-\;0}{2,500\;-\;2,211.821}= 0.2716

The estimate of gamma is

0.7691  −  0.27162,662.863  −  2,355.911\frac{0.7691\;-\;0.2716}{2,662.863\;-\;2,355.911}= 0.00162

The estimate of theta (per year) is

78.279  −  119.5790.3333\frac{78.279\;-\;119.579}{0.3333}= -123.9

The estimate of gamma is

\frac{0.7691\;-\;0.2716}{2,662.863\;-\;2,355.911}

2,662.863−2,355.911


0.7691−0.2716

​= 0.00162

The estimate of theta (per year) is

\frac{78.279\;-\;119.579}{0.3333}

0.3333


78.279−119.579

​= -123.9

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1 个答案

DD仔_品职助教 · 2022年05月10日

嗨，努力学习的PZer你好：


gamma衡量的是delta的变化比上股价的变化。delta的变化在第二个时间点才会出现，因为第一个时间点只有一个delta。

那么delta1=(328.791−78.279)​/(2,825.726−2,500)= 0.7691

delta2=(78.279−0)/(2,500−2,211.821)=0.2716

gamma=(delta1-delta2)/股价变化=(0.7691-0.2716)/(2662.863-2355.911)=0.00162


theta衡量的是期权价格与时间的变动关系，公式如下图：

theta=(78.279-119.579)/(1/3)=-123.9


这个计算了解即可，重点掌握希腊字母的含义




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NO.PZ2020021205000046问题如下Use the binomitree in Figure 14.7 of Chapter 14 to estimate the ltgammantheta of the optionThe lta estimate is202.098  −  38.8122,657.878  −  2,351.500\frac{202.098\;-\;38.812}{2,657.878\;-\;2,351.500}2,657.878−2,351.500202.098−38.812​=0.5330For gammwe calculate two ltfrom the nos the enof the secontime step. The lta from the upper nos, where the average inx is 2,662.863, is328.791  −  78.2792,825.726  −  2,500\frac{328.791\;-\;78.279}{2,825.726\;-\;2,500}2,825.726−2,500328.791−78.279​= 0.7691The lta calculatefrom the lower two nos, where the average inx is 2,355.911, is78.279  −  02,500  −  2,211.821\frac{78.279\;-\;0}{2,500\;-\;2,211.821}2,500−2,211.82178.279−0​= 0.2716The estimate of gamma is0.7691  −  0.27162,662.863  −  2,355.911\frac{0.7691\;-\;0.2716}{2,662.863\;-\;2,355.911}2,662.863−2,355.9110.7691−0.2716​= 0.00162The estimate of theta (per year) is78.279  −  119.5790.3333\frac{78.279\;-\;119.579}{0.3333}0.333378.279−119.579​= -123.9所以需要掌握所有greek letter的计算吗

2024-05-02 23:26 1 · 回答

NO.PZ2020021205000046问题如下Use the binomitree in Figure 14.7 of Chapter 14 to estimate the ltgammantheta of the optionThe lta estimate is202.098  −  38.8122,657.878  −  2,351.500\frac{202.098\;-\;38.812}{2,657.878\;-\;2,351.500}2,657.878−2,351.500202.098−38.812​=0.5330For gammwe calculate two ltfrom the nos the enof the secontime step. The lta from the upper nos, where the average inx is 2,662.863, is328.791  −  78.2792,825.726  −  2,500\frac{328.791\;-\;78.279}{2,825.726\;-\;2,500}2,825.726−2,500328.791−78.279​= 0.7691The lta calculatefrom the lower two nos, where the average inx is 2,355.911, is78.279  −  02,500  −  2,211.821\frac{78.279\;-\;0}{2,500\;-\;2,211.821}2,500−2,211.82178.279−0​= 0.2716The estimate of gamma is0.7691  −  0.27162,662.863  −  2,355.911\frac{0.7691\;-\;0.2716}{2,662.863\;-\;2,355.911}2,662.863−2,355.9110.7691−0.2716​= 0.00162The estimate of theta (per year) is78.279  −  119.5790.3333\frac{78.279\;-\;119.579}{0.3333}0.333378.279−119.579​= -123.9这个每个期权价格都是折现得出的吗？2351.5的话正常应该不执行，应该是0，为什么是38.812

2023-03-03 10:52 1 · 回答