In finance, gamma (represented by the Greek letter Γ) is a measure of the rate of change of an option’s delta with respect to changes in the underlying asset’s price. Essentially, it tells you how quickly the delta (which measures the change in an option’s price relative to the change in the underlying asset’s price) itself changes as the underlying asset’s price fluctuates.
Here’s a breakdown:
- Delta: Delta measures how much an option’s price will change for a one-point change in the underlying asset’s price.
- Gamma: Gamma measures how much the delta will change for a one-point change in the underlying asset’s price.
Formulas:
- Gamma = d(Delta) / d(Underlying Price)
- Gamma ≈ Δ Delta / Δ Underlying Price (approximation using finite differences)
Example:
Imagine you have a call option on a stock with a delta of 0.5. This means for every $1 increase in the stock price, the option’s price is expected to increase by $0.50. Now, assume the gamma for this option is 0.1. This means for every $1 increase in the stock price:
- Delta increases by 0.1 * $1 = $0.10.
- New delta becomes 0.5 + $0.10 = 0.6.
This signifies that for the next $1 increase in the stock price, the option’s price will likely increase by $0.60 instead of just $0.50.
Key takeaway:
- Higher gamma signifies larger and faster changes in the delta as the underlying price moves.
- Options closer to the money (strike price near current asset price) generally have higher gamma.
- Gamma is crucial for understanding the volatility of option prices and for strategies like delta-hedging.
Remember, this is a simplified explanation, and a more thorough understanding requires further study and considering other factors affecting option pricing.
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