Put Accumulator

Put Accumulator iconThe put accumulator is an extension of the eachway put. It is a digital put strip but with each strike having a different payout. Like the call accumulator, this is another strategy which, when bought out-of-the-money, can provide extremely high gearing. It also offers the speculator increasing rewards for an increasingly accurate forecast.

Put Accumulator Evaluation

Put Accumulator    =    R1 x Digital Put(K1) + R2 x Digital Put(K2) + R3 x Digital Put(K3) + R4 x Digital Put(K4)


K1 < K2 < K3 < K4


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

In the below example R1 =40%, R2 = 30%, R3 = 20% and R4 = 10%

Put Accumulator at Expiry

The put accumulator is a weighted average of four individual digital put option’s values. The sum of the ratios must come to 1, e.g. 0.4 + 0.3 + 0.2 + 0.1 =  1, these ratios providing a natural progression.

Many combinations can sum to 1 but the incremental increase of 0.1 lends itself to the betting terminology of ‘accumulator’ or ‘accy’ for short.

Put Accumulator Settlement Values
Figure 1 – Put Accumulator Settlement Values

The punter is increasingly rewarded by the put accumulator for the more accurate forecast of the market.

European Digitals Put Accumulator Delta Put Accumulator Gamma Put Accumulator Theta Put Accumulator Vega

Put Accy Over Time

Figure 2 shows the impact of the passage of time on the put accumulator. The strategy is a weighted average of the individual digital put options. The profiles closely map each other until the final hours and minutes prior to expiry. As with the eachway put option this strategy can be designed to have more or less gearing by adjusting the distance between strikes.

Put Accumulator w.r.t. Time to Expiry
Figure 2 – Put Accumulator w.r.t. Time to Expiry

The call and put accumulator offer a smooth price trajectory, apart from over the very last minutes. This feature is acknowledged as has already been seen by a low call accumulator delta and put accumulator delta. It is only with 0.01-days to expiry that the profile looks remotely like the expiry profile of the digital put. The accumulator is a great deal less risky for the market-maker as well as the speculator who buys it out-of-the-money. Why?

  • the profile reflects a low delta which means directional risk at the trade’s inception is low.
  • the vega risk is low as witnessed by Figure 3, and
  • at expiry the maximum incremental change is just 30 (between the two highest strikes) which vastly reduces ‘pin’ risk1.

With these risks taken out of the equation the market-maker is likely to produce highly competitive, tight bid/ask quotes.

Put Accy and Volatility

Figure 3 shows the effect of changes in implied volatility on the put accumulator. Here we see the put accumulator moving very closely in tandem over a wide range of volatilities from just 2% to 18%.

Put Accumulator w.r.t. Volatility
Figure 3 – Put Accumulator w.r.t. Volatility

The put accumulator value is an average price like the binary put strip and eachway put. This means the put accumulator is not greatly influenced by volatility changes. Subsequently we can be confident in assuming low put accumulator vega values.


We can conclude that from Figures 2 & 3 this strategy is not designed for use as a theta or vega play; the put accumulator is an out-and-out directional instrument with a P&L profile unlike any other option at expiry.

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