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SkipperLin · 2020年06月17日

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=ln(41/40)+(0.05+0.222/2)×0.750.220.75=0.4217d1=\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

1 个答案

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。