Greeks and Risk Factors
Greeks measure sensitivity of prices to well-defined risk factors like spot, rates, and volatility.
Greeks such as delta, gamma, vega, and rho describe how derivative prices respond to small changes in underlying risk factors.
Risk factors are chosen coordinates (spot, curve pillars, vol points) that risk limits and aggregation are built on.
In a library, the risk engine wraps pricers with bump logic or AAD to compute Greeks consistently across products.
A coherent factor set makes risk reports and limits comparable across desks and asset classes.
This curve shows option PV as a function of a single risk factor. At the current point you see the delta tangent and a faint delta+gamma approximation band. Use the controls to switch factor type and see how a small bump propagates into price.
Delta is the local slope of PV with respect to a chosen risk factor; gamma is the local curvature. For a tiny bump, delta alone explains the move; as the bump grows, curvature starts to matter and the delta+gamma approximation tracks the true PV better.
The same geometry applies whether your factor is spot, a rate pillar, or a vol point. The practitioner’s view: Greeks are not mystical, they are just derivatives along a chosen factor coordinate system. Good risk reports start by choosing sensible coordinates and then using these local slopes and curvatures consistently across the book.