Dear all,

I'm wondering if my calculations of the following problem is correct:

10 000 call options on S&P500

Characteristics of the option:

Start date: March 31st 2011

Type: European

Maturity: May 31st 2011

Strike Price: 1400

1 option contract gives the right to buy 1 S&P500 index

This is how far I got:

Delta of a call option is positive.

∆ (call)= N(d1)

d1 = (ln(S0/K)+(r+σ^2/2)T)/(σ√T)

First we need to find the respective parameters

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

Delta of a futures contract is e^rT

e^(0,0015)*(2/12) = 0,166916854

Number of future contracts =

= (number of options * delta call)/delta future

= (10000*0,194801472167245)/0,166916854

= 11670,56934

So in order to create a delta neutral portfolio the investor should go short in 11670,56934.

Your help is much appreciated.

I'm wondering if my calculations of the following problem is correct:

10 000 call options on S&P500

Characteristics of the option:

Start date: March 31st 2011

Type: European

Maturity: May 31st 2011

Strike Price: 1400

1 option contract gives the right to buy 1 S&P500 index

**1) So, what is the amount of CME S&P 500 Futures traded on the Chicago Mercantile Exchange (www.cme.com ) that I need, in order to make this portfolio delta neutral?**This is how far I got:

Delta of a call option is positive.

∆ (call)= N(d1)

d1 = (ln(S0/K)+(r+σ^2/2)T)/(σ√T)

First we need to find the respective parameters

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

Delta of a futures contract is e^rT

e^(0,0015)*(2/12) = 0,166916854

Number of future contracts =

= (number of options * delta call)/delta future

= (10000*0,194801472167245)/0,166916854

= 11670,56934

So in order to create a delta neutral portfolio the investor should go short in 11670,56934.

**Is this correct or should I somehow take into account the contract size of the future ($250 x S&P 500 futures price) ?**Your help is much appreciated.

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