掌握计算

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

解释：

The delta estimate is

$\frac{202.098\;-\;38.812}{2,657.878\;-\;2,351.500}$ =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

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

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

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

The estimate of gamma is

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

The estimate of theta (per year) is

$\frac{78.279\;-\;119.579}{0.3333}$ = -123.9

所以需要掌握所有greek letter的计算吗

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品职答疑小助手雍 · 2024年05月03日

同学你好，本题这种定义式类的计算还是需要掌握的，本题考察的全是定义式。

比如delta是期权对资产的敏感性，gamma是delta的敏感性，theta是期权价格对时间（期限）的敏感性。都是直接拿期权价格变化除以对应参数的变化的式子。

其他通过模型去计算希腊字母的，只要掌握BSM模型里对delta的计算即可。

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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

NO.PZ2020021205000046 问题如下 Use the binomitree in Figure 14.7 of Chapter 14 to estimate the ltgammantheta of the option The 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 The estimate of gamma is\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) is\frac{78.279\;-\;119.579}{0.3333}0.333378.279−119.579= -123.9

2022-05-10 18:12 1 · 回答

掌握计算

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