As we build our portfolios and structure our positions, we work hard tofor our success, such as time . However, we inevitably still end up with some directional component to our trades, either intentionally or unintentionally. Well, when it comes to direction, delta effectively measures our degree of direction, and gamma captures the movement of delta. As a result, we are trying to avoid “gamma risk”, or gamma’s tendency to expand as we near expiration.
If we, we can mathematically express the foundations of gamma risk. Specifically, gamma risk would be best represented by “color”, or the derivative of gamma with respect to time. As we see, this equation for color shows us just how gamma does indeed change as our time evaporates and expiration draws closer.