# How to correctly calculate the number of options in pair trading?

#### AlexCZ

##### Newbie
3 0
For example, I have pair GDX*231-GLD*145. I want to take deviation and use ATM options for this. I want to buy a put GDX and buy a call GLD. Ratio in this pair GDX and GLD 1.59. Do I need to use this ratio in options? Or I need to correct this ratio using options gamma and delta? Or use one gamma? Or just take options in the ratio 1.59?

#### Windlesham1

##### Well-known member
438 30
Yes -have no idea what you are saying but if 1.59 is magical use it.

#### ARBinstruktor

##### Junior member
15 2
Your ratio is a simple nominal value hedge, assumming perfect correlation. Another approach would be a statistical hedge, using the beta-coeffecient.

1.59 assumes that GDX and GLD have identical volatility, which is of course not the case. If you look for a vola hedge you have to consider Vola(GDX)/Vola(GLD). If you also take the correlation into consideration; you have the beta.

BUT that would not help either. What you need is a descent scenario: what will GDX do when GLD does x, if you have decided how many possible paired results (x/y) you want to consider, you can check what (final) option prices you would get per scenario outcome.
Having these option prices you can start to look for combinations, which bring you a profit over all outcomes, or at least for your favoured outcomes.

1. GDX = Function(GLD) eg %GDX = alpha + beta*%GLD

2.
.........................................................................................
................................................................................
----------------------------------> GLD1 future -------------> GDX1 fut
---------------------------> GLD2 fut -------------> GDX2 fut
GLD today --> GLD3 fut -----------> GDX3 fut
-------------------------------> GLD4 fut ---------------> GDX4 fut
-------------------------------------------> GLD5 fut -------------> GDX5 fut
..........................................................................................
................................................................................................

3. GDX? fut = GDX today * (1 + alpha + beta* %GLD? fut)

4. PUT? fut =~ Max(X-GDX? fut; 0)

5. CALL? fut =~ Max(GLD? fut -X; 0)

6. (PUT? fut - PUT today) + HR * (CALL? fut -CALL today) > or >/= 0 for all ? = 1 .... n (=5)

that is a slight hint to the correct approch

Windlesham1

#### Windlesham1

##### Well-known member
438 30
Your ratio is a simple nominal value hedge, assumming perfect correlation. Another approach would be a statistical hedge, using the beta-coeffecient.

1.59 assumes that GDX and GLD have identical volatility, which is of course not the case. If you look for a vola hedge you have to consider Vola(GDX)/Vola(GLD). If you also take the correlation into consideration; you have the beta.

BUT that would not help either. What you need is a descent scenario: what will GDX do when GLD does x, if you have decided how many possible paired results (x/y) you want to consider, you can check what (final) option prices you would get per scenario outcome.
Having these option prices you can start to look for combinations, which bring you a profit over all outcomes, or at least for your favoured outcomes.

1. GDX = Function(GLD) eg %GDX = alpha + beta*%GLD

2.
.........................................................................................
................................................................................
----------------------------------> GLD1 future -------------> GDX1 fut
---------------------------> GLD2 fut -------------> GDX2 fut
GLD today --> GLD3 fut -----------> GDX3 fut
-------------------------------> GLD4 fut ---------------> GDX4 fut
-------------------------------------------> GLD5 fut -------------> GDX5 fut
..........................................................................................
................................................................................................

3. GDX? fut = GDX today * (1 + alpha + beta* %GLD? fut)

4. PUT? fut =~ Max(X-GDX? fut; 0)

5. CALL? fut =~ Max(GLD? fut -X; 0)

6. (PUT? fut - PUT today) + HR * (CALL? fut -CALL today) > or >/= 0 for all ? = 1 .... n (=5)

that is a slight hint to the correct approch
I just trade and make a profit! I stick with the index- no warnings,divi's, CEOs getting arrested, massive gold reserves being flogged off. Liquid market -why make things complicated?

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