Finance Gamma Wikipedia

Gamma in finance, as defined by Wikipedia and across financial literature, is a crucial second-order derivative that measures the rate of change of an option's delta with respect to a change in the underlying asset's price. It quantifies how much the delta, which represents the option's sensitivity to price changes in the underlying, is expected to move for every one-unit change in the underlying's price. A high gamma indicates that the delta is highly sensitive to price fluctuations in the underlying. This means that as the underlying asset's price moves, the option's delta will change significantly. Conversely, a low gamma suggests the delta is less sensitive, and smaller adjustments to the hedge are needed as the underlying asset price changes. Traders monitor gamma to understand the potential hedging adjustments required to maintain a delta-neutral position. A delta-neutral portfolio aims to be insensitive to small price movements in the underlying asset, protecting the portfolio's value. However, because the delta itself changes with price movements, gamma reveals the speed at which the delta-neutral hedge needs to be rebalanced. Imagine a portfolio of options with a high gamma. As the underlying asset price moves, the portfolio's delta will quickly change, requiring more frequent adjustments to maintain delta neutrality. These adjustments involve buying or selling the underlying asset to offset the delta's change. The higher the gamma, the more frequent and potentially larger these adjustments need to be. This rebalancing process is commonly referred to as "gamma scalping" or "dynamic hedging." Gamma is typically highest for at-the-money options, which are options whose strike price is close to the current market price of the underlying asset. As an option moves further in-the-money (where the strike price is favorable) or out-of-the-money (where the strike price is unfavorable), gamma tends to decrease. The expiration date also affects gamma; options closer to expiration usually exhibit higher gamma, as their price becomes more sensitive to the underlying's movements as the payoff becomes imminent. Understanding gamma is vital for option traders and portfolio managers for several reasons. Firstly, it allows them to better manage and control the risk associated with their option positions. By monitoring gamma, they can anticipate the magnitude of adjustments required to maintain their desired risk profile. Secondly, it enables more accurate pricing of options. Gamma is a key input in option pricing models, like the Black-Scholes model, influencing the theoretical value of the option. Thirdly, gamma provides insights into potential profit opportunities. Dynamic hedging, guided by gamma, can generate profits by repeatedly buying low and selling high (or vice versa) as the underlying asset price fluctuates. However, it's important to note that managing gamma comes at a cost. Each rebalancing transaction incurs brokerage fees, and frequent adjustments can be expensive. Moreover, unexpected price jumps in the underlying asset can make it difficult to maintain a perfectly delta-neutral position, leading to potential losses. Therefore, traders must carefully weigh the benefits of hedging against the associated costs.