Delta-Gamma – Delta-Gamma Approximation Helps with Derivative Analysis

Okay, if you are looking for “delta gamma” you are looking for one of two things: the Delta Gamma sorority or the Greek options used in financing. This article works to explain the delta-gamma approximation in investing analysis.

Derivatives make up a significant part of the portfolio value of major investors as well as average ones. Derivative instruments are those financial instruments that get their value from the value of another financial instrument. For example, a stock option is a derivative because it gets its real value from the current value of the stock. The stock itself is a cash instrument, not derivative. The trading value of the derivative can vary in different ways from the actual underlying instrument from which it gets its underlying value.

To understand the way that the value of a derivative will fluctuate based on the value of the underlying instrument, financial analysts developed different ways to measure the sensitivity of the derivative to the changes in value of the underlying security. Two of those measurements are the delta and the gamma.

Delta measures the sensitivity of an option’s theoretical value to the underlying change in price of the asset. There are two ways to display delta. It is either between -1 and 1 or between -100 and 100. In either measurement, the idea is to show how much value you would gain or lose if the underlying financial instrument gains $1 of value.

Gamma is a calculus formula that compares an entire portfolio’s value with the value of an underlying asset. The value of gamma is actually the second derivative of the portfolio’s value divided by the value of the underlier.

When brought together, the delta and gamma offer a good approximation of how much a portfolio’s value will change in response to underlying asset value changes. To calculate the delta-gamma approximation, there are several items to consider:

  1. Original stock price
  2. Stock price after change
  3. Call option price
  4. Different from original stock price and stock price after change
  5. Delta calculation
  6. Gamma calculation

The formula used is as follows:

C(St+h) = C(St) + є∆(St) + (1/2)є2Γ(St)

This is a theoretical calculation. However, many investors find this approximation, in combination with other calculation can provide a good indication of what will happen to a portfolio if an underlying asset value changes. The delta and gamma calculations alone give great information. Together, they are even better.

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