The put accumulator is an extension of the eachway put. It is a binary 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.

European Binary Options | Put Accumulator Delta | Put Accumulator Gamma | Put Accumulator Theta | Put Accumulator Vega |

### Put Accumulator Evaluation

Put Accumulator = R_{1} x Binary Put(K_{1}) + R_{2} x Binary Put(K_{2}) + R_{3} x Binary Put(K_{3}) + R_{4} x Binary Put(K_{4})

where:

K_{1} < K_{2} < K_{3} < K_{4}

and:

R_{1} > R_{2} > R_{3} > R_{4} and R_{1} + R_{2} + R_{3} + R_{4} = 1

In the below example R_{1} =40%, R_{2} = 30%, R_{3} = 20% and R_{4} = 10%

### Put Accumulator at Expiry

The put accumulator is a weighted average of four individual binary 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.

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

### 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 binary 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.

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 binary 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’ risk
^{1}.

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%.

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.

^{1 }Pin Risk is the market-makers nightmare at expiry.

For example: A market-maker is short or long a bucket load of binary calls with strike 100.00. The underlying price is 99.99 bid, offered at 100.01. If the asset is deemed to be 99.99 at expiry the option is worthless. At 100.00 it is worth 50. At 100.01 the option is worth 100. The market maker could be subject to a huge swing in P&L. The art of risk management is worthless. Welcome to the ‘witching hour’!

By: Hamish Raw