Gamma
Gamma (Γ) is an options risk metric that describes the rate of change in an option's delta per one-point move in the underlying asset's price. Delta is how much an option's premium (price) will change given a one-point move in the underlying asset's price. Therefore, gamma is a measure of how the rate of change of an option's price will change with fluctuations in the underlying price.
The higher the gamma, the more volatile the price of the option is.
Gamma is an important measure of the convexity of a derivative's value in relation to the underlying asset. It is one of the "options Greeks" along with delta, rho, theta, and vega. These are used to assess the different types of risk in options portfolios.
Definition: Gamma (Γ) is a measure of the risk associated with options, describing the rate of change in the option's value as the underlying asset's price changes by one point. Delta refers to the change in the option's premium (price) when the underlying asset's price changes by one point. Therefore, Gamma is an indicator of how quickly the option's price changes with fluctuations in the underlying asset's price. The higher the Gamma, the greater the option's price volatility.
Origin: The concept of Gamma originated from the development of the financial derivatives market, particularly the evolution of option pricing models. The Black-Scholes model, introduced in the 1970s, provided a theoretical foundation for option pricing, and the Greek letter indicators system gradually became more refined, with Gamma being a crucial component.
Categories and Characteristics: Gamma is primarily used to measure the price sensitivity of options, especially in the short term. Options with high Gamma values typically exhibit higher volatility, making them suitable for short-term traders; options with low Gamma values have less volatility, making them suitable for long-term holders. Gamma values significantly increase near the option's expiration date, especially when the option is at-the-money.
Specific Cases: 1. Suppose an investor holds a call option with an underlying asset price of $100, a Delta of 0.5, and a Gamma of 0.1. If the underlying asset price increases by $1, the Delta will increase to 0.6, making the option's price change more significant. 2. Another investor holds a put option with an underlying asset price of $50, a Delta of -0.4, and a Gamma of 0.05. If the underlying asset price decreases by $1, the Delta will change to -0.45, and the option's price will adjust accordingly.
Common Questions: 1. Why does Gamma increase near the option's expiration date? Because near the expiration date, the time value of the option rapidly decreases, increasing the price sensitivity to the underlying asset's price. 2. How can Gamma be used for risk management? Investors can control Gamma by adjusting the number of options in their portfolio, thereby managing the portfolio's volatility.
