# Put Accumulator Gamma The put accumulator gamma describes the change in value of a put accumulator delta due to a change in the underlying price. This gamma is the first derivative of the put accumulator delta with respect to a change in underlying price. It is depicted as: where Δ is the put accumulator delta value and S is the asset price.

### Evaluating Put Accumulator Gamma

Put Accumulator Gamma = R1 x Digital Put Gamma(K1) + R2 x Digital Put Gamma(K2)

+ R3 x Digital Put Gamma(K3) + R4 x Digital Put Gamma(K4)

where the terms are the individual digital put gamma with strikes K1, K2, K3 & K4 respectively.

Where:

K1 < K2 < K3 < K4

and where:

R1 + R2 + R3 + R4 = 1  and R1 > R2 > R3 > R4

The payouts in the below examples are:

R1 = 40%, R2 = 30%, R3 = 20% and R4 = 10%

### Put Accy Gamma Over Time

The put ‘accy’ delta is displayed against time to expiry in Figure 1. The 0.1-day profile shows the volatility of this metric with the profile on a switchback tide through the strikes.