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JR · 2021年09月13日

咨询

NO.PZ2017121101000029

问题如下:

Stanley Kumar Singh, CFA, is the risk manager at SKS Asset Management. He works with individual clients to manage their investment portfolios.

A third client, Wanda Tills, does not currently own Walnut shares and has asked Singh to explain the profit potential of three strategies using options in Walnut: a long straddle, a bull call spread, and a bear put spread. In addition, Tills asks Singh to explain the gamma of a call option. In response, Singh prepares a memo to be shared with Tills that provides a discussion of gamma and presents his analysis on three option strategies:

Strategy 1: A long straddle position at the $67.50 strike option

Strategy 2: A bull call spread using the $65 and $70 strike options

Strategy 3: A bear put spread using the $65 and $70 strike options

Based on the data in Exhibit 2, Singh would advise Tills that the call option with the largest gamma would have a strike price closest to:

选项:

A.

$ 55.00.

B.

$ 67.50.

C.

$ 80.00.

解释:

B is correct.

The $67.50 call option is approximately at the money because the Walnut share price is currently $67.79. Gamma measures the sensitivity of an option’s delta to a change in the underlying. The largest gamma occurs when options are trading at the money or near expiration, when the deltas of such options move quickly toward 1.0 or 0.0. Under these conditions, the gammas tend to be largest and delta hedges are hardest to maintain.

0.63和0.37接近0.5的程度不都是0.13吗?为什么选0.63

1 个答案
已采纳答案

Hertz_品职助教 · 2021年09月13日

嗨,努力学习的PZer你好:


同学你好~

1.     根据表格的第一行信息我们可知当前股价是67.79。然后我们说一个期权在ATM的时候,gamma是最大的,本题问的也正是找一个gamma最大的期权,即我们需要找一个最ATM的期权。

2.     判断期权是ATM,ITM或者是OTM,是比较股价S0和行权价格的。而当二者相等的时候,不论call还是put都是ATM的状态。所以我们应该看表格中的第一列行权价,然后和67.79相比,哪一个和67.79最接近,这个期权就越是ATM的,gamma也就最大。所以看到只有67.5是和67.79是最近的,因此其具有最大的gamma。

3.     你的思路应该是从0.5delta的角度来入手的哈,思路应该是gamma最大的时候是ATM的时候,ATM的时候期权的delta是0.5,因此就找delta距离0.5最近的期权。

这里需要注意我们说期权在ATM的时候delta是0.5,其实是一种不太准确的说法,确切的说应该是delta在0.5附近。但是可以确定的是只要股价S0=行权价X,就一定是ATM的。所以我们在做这种题目的时候要根据股价和行权价之间来判断期权的状态是否是ATM的。而不能从0.5delta的角度来入手哈

逻辑一般是S0=X → 期权是ATM的 → 该期权的delta=0.5

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