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水瓶公主 · 2023年03月03日

每个期权的价格不是s-x吧

  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

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

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

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1 个答案

李坏_品职助教 · 2023年03月03日

嗨，爱思考的PZer你好：


这是个欧式期权，欧式期权不能提前行权，所以不需要去判断2351.5的时候是否应该为0。它对应的38.812就是用2500的78和2211的0折现出来的。


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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 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