Gamma How to Calculate Gamma: Step by Step

  • Thread starter John Creighto
  • Start date
In summary, to go from the equation \Gamma^k_{ij}=-\bold{e}_j \cdot D_i \bold{e}^k to D_i \bold{e}^k = \Gamma ^k_{ij} \bold{e}^j, we can use the fact that \textbf{v} \cdot \textbf{u} = \textbf{u} \cdot \textbf{v} and \textbf{e}_j \textbf{e}^j = \textbf{1} to rewrite the equation as \Gamma^k_{ij} \textbf{e}^j = -D_i\textbf{e}^
  • #1
John Creighto
495
2
Can someone explain to me how to go from

[tex]\Gamma ^k_{ij}=-\bold{e}_j \cdot D_i \bold{e}^k[/tex]

To

[tex]D_i \bold{e}^k = \Gamma ^k_{ij} \bold{e}^j \ \cdot \ \ [/tex]
 
Physics news on Phys.org
  • #2
Try this:
[tex]\Gamma^k_{ij} = -\textbf{e}_j \cdot D_i\textbf{e}^k[/tex]
[tex]\Gamma^k_{ij} = -D_i\textbf{e}^k \cdot \textbf{e}_j [/tex] because [tex] \textbf{v} \cdot \textbf{u} = \textbf{u} \cdot \textbf{v} [/tex]
[tex]\Gamma^k_{ij} \textbf{e}^j = -D_i\textbf{e}^k \cdot \textbf{e}_j \textbf{e}^j[/tex]
[tex]\Gamma^k_{ij} \textbf{e}^j = -D_i\textbf{e}^k \cdot \textbf{1}[/tex] because [tex] \textbf{e}_j \textbf{e}^j = \textbf{1} [/tex]
[tex]\Gamma^k_{ij} \textbf{e}^j = -D_i\textbf{e}^k [/tex] because [tex] \textbf{e} \cdot \textbf{1} = \textbf{e} [/tex]
Well, I got close, but I don't know how to drop the minus sign. For the identity tensor, I believe [tex] \textbf{1} \cdot \textbf{v} = \textbf{v} \cdot \textbf{1} [/tex] is true (though not true for other second rank tensors)
 
Last edited:
  • #3
I think you are right, Davidcantwell!
[tex]
\Gamma^k_{ij} \textbf{e}^j = -D_i\textbf{e}^k
[/tex]
implies
[tex]
\Gamma^k_{ij} = -\textbf{e}_j \cdot D_i\textbf{e}^k
[/tex]
The original statement seems not correct.
 

Related to Gamma How to Calculate Gamma: Step by Step

What is Gamma?

Gamma is a measure of the rate of change in an option's delta for a one-point change in the underlying asset's price. It is used to assess the risk associated with changes in an option's price due to changes in the underlying asset's price.

Why is Gamma important?

Gamma is important because it helps traders and investors understand the potential risks and rewards associated with options trading. It also helps in making informed decisions about when to buy or sell options.

How is Gamma calculated?

Gamma is calculated by taking the derivative of an option's delta with respect to the underlying asset's price. It can also be calculated by dividing the change in an option's delta by the change in the underlying asset's price.

What factors affect Gamma?

The main factors that affect Gamma are time to expiration, strike price, and volatility. As the expiration date approaches, Gamma tends to increase. As the strike price moves closer to the current price of the underlying asset, Gamma also tends to increase. And as volatility increases, so does Gamma.

How can I use Gamma in my trading?

Gamma can be used in a number of ways in trading. It can help determine the level of risk associated with an option, identify potential profit opportunities, and assist in creating a well-balanced portfolio. It is important to understand Gamma and its relationship with other option parameters in order to effectively use it in trading strategies.

Similar threads

  • Differential Geometry
Replies
9
Views
3K
  • Advanced Physics Homework Help
Replies
6
Views
349
  • Advanced Physics Homework Help
Replies
10
Views
747
  • Differential Geometry
Replies
1
Views
1K
  • Differential Geometry
Replies
15
Views
4K
  • Advanced Physics Homework Help
Replies
0
Views
656
  • Chemistry
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
424
  • Cosmology
Replies
9
Views
1K
Replies
6
Views
1K
Back
Top