d1=0.2921,怎么推出 ndi的呀

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=$\frac{\ln(40/40)\;+\;(0.05\;+\;0.22^2/2)\;X\;0.75}{0.22\sqrt{0.75}}\\$= 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.