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.
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.
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.
| European Digitals | Eachway Puts | Eachway Put Gamma | Eachway Put Theta | Eachway Put Vega |
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.
If one uses delta as a gauge to the aggressive nature of a strategy then the eachway put is clearly a lot more conservative; but then again, that is in comparison to the punchiest strategy available on financial markets.