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papher · 2020年06月24日

问一道题:NO.PZ2020021205000039

问题如下:

What is the delta of a short position on 100,000 call options on a stock with a market price and strike price of USO 40 when the risk-free rate is 5%, the volatility is 22%, and the time to maturity is nine months?

选项:

解释:

The delta of a long position in one option is N(d1 ). In this case:

d1=ln(40/40)  +  (0.05  +  0.222/2)  X  0.750.220.75\frac{\ln(40/40)\;+\;(0.05\;+\;0.22^2/2)\;X\;0.75}{0.22\sqrt{0.75}}\\= 0.2921

so that N(d1 ) = 0.615. The delta of a short position in one option is -0.615 and the delta of a short position in 100,000 options is -61,500.

可以用 S=K时 ,delta = 0.5 或者 -0.5 这样理解 吗?

1 个答案

品职答疑小助手雍 · 2020年06月24日

嗨,努力学习的PZer你好:


不能,这题给的考点明显就是直接考BSM的公式啦,还是要带公式的

而且,一般带有rf作为风险中性的期望收益的话,S=K时delta等于0.5就不成立了,此时一般delta会大一些。因为S经过rf的期望增加会更可能大于K。

你可以做个小实验,加深理解,把公式放在excel里,调整rf的变化,你会发现rf 越小,这题的delta也越小。


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