为什么不是short 4800？

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.