# BS and delta hedging questions

I have two related questions concerning Black Scholes and delta hedging. I thought about this two questions, but I could not come up with an answer, so maybe you guys & girls can help me:

1. If an option is at the money, how can the Black Scholes price be calculated in a very fast way (possibly without any big calculations)?

2. If an option is at the money, how many shares do you have to buy in order to delta-hedge?

• Is this a homework assignment? These are the most commonly presented results in any textbook on options pricing. – chrisaycock Dec 31 '12 at 12:14

2. You have to buy/sell $\Delta$ shares. $\Delta_{ATM} \approx 0.5$.
• actually, asset prices do not follow arithmetic brownian motion in .4 *S*$\sigma * \sqrt{T}$, it is still geometric brownian motion. just do a simple taylor expansion on B-S formula and you will see – Andrew Dec 31 '12 at 21:25