Sorry for this way of communication but I tried but this seem to be the only way left.
Zman492, I am really appreciate for your help. But their is some part i still confuse. I really do hope you can take a look at the question again and explain in more detail.
Question:
Say for example:
Simulation date: Mars 31st 2011
Using 10 000 call options on S&P500 whose characteristics are
Exercise type: European
Maturity: May 31st 2011
Strike: 1400
What should I do if I want to know how many future contract CME S&P 500 Futures I need to get a delta hedged portfolio?
After one month, what should I do if Strike price of S&P 500 go up 1%, 10%, what if it goes down by 1%,10%.
Do you have any comments in this portfolio?
Here is my calculation so far.
As I understand delta for future contract is always equal 1. So here is how i calculate delta for option positon:
∆ (call)= N(d1)
d1 = (ln(S0/K)+(r+σ^2/2)T)/(σ√T)
I can find these informations
S0 = 1325,83 on 31/03/2011
K = 1400
r = 0,0015 is the annual treasury bill rate at 31 March
σ= 0,149 (Annualizing gives 0,0094*SQRT252 = 0,149)
T = 2/12
Now we can calculate delta:
d1 = (ln((1325,83 )/1400)+(0.0015+〖0,149〗^2/2)*(2/12))/(0,149√((2/12)))
d1 = -0,86034
N(d1)= 0,194801
And i get stuck here as I dont understand about future contract CME S&P 500 .
Thanks for reading.
Answers & Comments
Verified answer
Well you rang him, but Zman just doesn't answer. Maybe he is busy.
<<<If i have 1 name option, is it i need one future contract with a view to build a delta hedged portfolio.>>> No. Throughout the time of the simulation the S&P 500 index used to be well under 1400 so the decision options had been out of the money, so we all know the delta for the option could be less than zero.5. For example purposes, shall we say it was zero.2. If the underlying of the contract was once one futures contract, considering that you realize the delta of the futures contract is 1.Zero you can need one futures contract for every 5 choices. (1.0 / zero.2 = 5) considering that each have a constructive delta you can need to be long one role and brief the opposite. <<<And say at after a month from the simulation date, what's the influence of the delta hedged portfolio if the strike of S&P500 go up or down (+-1%,+-10%)>>> without doing the maths to affirm this, i might expect a 1% transfer would not have a large affect on the option's delta, but the passage of time would have reduced it so you could either ought to increase the number of choices or scale back the number of futures contracts to stay delta neutral. Since a 10% decline within the index would lessen the delta of the option additional, you possibly can ought to make a an identical adjustment to stay delta impartial. A 10% expand within the index would put the alternative in the cash, with a delta over 0.5, so you possibly can either must develop the number of futures contracts or minimize the number of option contracts to remain delta impartial. <<<And do you suppose this portfolio is just right?>>> there may be no longer enough understanding to tell.