# Eachway Put Delta Eachway put delta describes the change in the fair value of an eachway put due to a change in the underlying price. The delta is the first derivative of the eachway put with respect to a change in underlying price and is depicted as: where  S is the underlying price and P the eachway put value.

### Evaluating the Delta

Delta = R1 x Digital Put Delta(K1) + R2 x Digital Put Delta(K2)

where the first term and second terms are the digital put delta with strikes K1 and K2 respectively. K1 < K2 and R1 + R2 = 1 and R1 ≥ R2.

### Eachway Put Delta Over Time

The delta is displayed against time to expiry in Figures 1a and 1b. The troughs of the deltas of the individual strikes is evident. Figure 1a – Eachway Put Delta w.r.t. Time to Expiry 100-50-0

A pay out structure of 100:25:0 equates to a delta ratio of 75% and 25% lower strike to upper strike as the 1.0 day profile illustrates. Figure 1b – Eachway Put Delta w.r.t. Time to Expiry 100-25-0

Subsequently, the deltas of the individual puts are a great deal higher in absolute terms than the eachway put deltas. For example, in Figure 1b at 98.50 the delta has fallen to -0.82. The 98.50 digital put delta with same variables would be -1.09. The difference of -0.27 is the height of the 0.5 day delta at 101.00. In effect one can conclude that the sum of the eachway deltas equal the delta of the outright digital put delta.

### Eachway Put Delta and Volatility

Figures 2a and 2b provide the delta over a range of implied volatilities. As implied volatility falls from 18% the profiles only gradually reflect the positions of the individual strike prices. This abruptly changes at 6 where the volatility falls to 2% with the troughs at the strikes become more pronounced.