问一道题：NO.PZ2020021205000065

问题如下：

a short position on 100,000 call options on a stock with a market price and strike price of USD 40 when the risk-free rate is 5%, the volatility is 22%, and the time to maturity is nine months what trade should be done to create a delta-neutral position? (Assume that the trader has no other positions dependent on the stock price.) If the stock price increases to USD 41 within a very short period, what further trade is necessary?

选项：

解释：

The trader should buy 61,500 shares of the stock to create a delta-neutral position. If the stock price then moves up to USD 41:

$d1=\frac{\ln(41/40)+(0.05+0.22^2/2)\times0.75}{0.22\sqrt{0.75}}=0.4217$

and N(d1 ) = 0.663. The delta of the option position is -66,300 and a further 4,800 shares should be purchased.

请问一下为什么在第一种情况下：delta计算完为-61,500，要去buy 61500 stock 而不是stort stock？我以为是按照符号看long short的。谢谢

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小刘_品职助教 · 2020年06月17日

同学你好，

因为公式的计算是基于long position on call option的，现在题目里是short position；所以就负负得正了。

这种题目buy 还是 sell ，建议直接根据你的头寸方向来判断更快。

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NO.PZ2020021205000065问题如下a short position on 100,000 call options on a stowith a market prianstrike priof US40 when the risk-free rate is 5%, the volatility is 22%, anthe time to maturity is nine months whtra shoulne to create a lta-neutrposition? (Assume ththe trar hno other positions pennt on the stoprice.) If the stopriincreases to US41 within a very short perio whfurther tra is necessary? The trar shoulbuy 61,500 shares of the stoto create a lta-neutrposition. If the stoprithen moves up to US41:=ln⁡(41/40)+(0.05+0.222/2)×0.750.220.75=0.4217=\frac{\ln(41/40)+(0.05+0.22^2/2)\times0.75}{0.22\sqrt{0.75}}=0.4217=0.220.75ln(41/40)+(0.05+0.222/2)×0.75=0.4217anN( ) = 0.663. The lta of the option position is -66,300 ana further 4,800 shares shoulpurchase上一题是-61500，这题是-66300，数量增加了，那不是应该再short 4800个call么？

2022-03-19 23:22 1 · 回答

NO.PZ2020021205000065 因为题目中stoprice=strike price，当做short ATM Call 来看，认为lta 是 -0.5。请问这种想法为什么不对？为什么何用BSM计算的公式结果不一样？谢谢。

2021-07-09 11:35 1 · 回答

4800share是如何得出的

2020-03-11 17:23 1 · 回答

老师你好，61500是怎么算出来的？不知道要lta neutr头寸相反对冲

2020-02-26 18:17 1 · 回答

问一道题：NO.PZ2020021205000065

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