lot of questions (about greek)

[Julianlapoutre]

Hi everybody, first of all, can you tell me which book will fit what i'm looking for, i know Hull but there is not all answer.

For example i don't find the answer for :

i have sold 100 puts, strike = 100 and maturity 3 months on a stock wich worth 100 to bet delta hedge i have to :

1)Buy 50 stocks
2)Sell 50 stocks
3) Buy 30 stocks

I think that answer is sell 50 stocks, because i have understood that i have to sell, but i dont know why 50 ?!

An other example :

I have solde a call and i'm delta hedged my position is :
1) Gamma+/vega-
2) Gamma+/vega+
3) Gamma-/vega-

I would like to say that vega is always positif, but i know that answer is the third but i don't understand why

last question (i have a lot ...)

I'm long on a call, strike = 100; Spot = 100 and i'm delta hedged. Spot rise to 110 to delta hedge i have to
1) Buy stock
2) Sell stock
3) I do nothing i'm already delta hedged

Answer is 2) but i'm not sure

thanks for help guys

 

[aaronhotchner]

There is no way to know the hedge ratio (delta) just from knowing S = 100, K = 100, T = 3 mo. But you sold puts, so your delta is (put delta) * -100, and put delta is negative, so you are positive delta. You would naturally need to sell to be delta neutral, and "sell 50 stocks" is the only option which includes selling.

You sold a call and delta hedged. Gamma and vega are always positive, and you sold both of them, so you are short gamma and short vega.

You are long a call with positive gamma. As the stock price increases, delta increases due to gamma. You need to sell delta to go back to delta = 0, so you sell stock.