Call Accumulator

call accumulatorThe call accumulator is an extension of the eachway call. There are four strike prices with the settlement prices at 0, 10, 30, 60 and 100 as outlined in Figure 1. This is a strategy which, when bought out-of-the-money, can provide extremely high gearing, and increasingly rewards the speculator for an increasingly accurate forecast.

Call Accumulator GreeksBelow 1st StrikeBetween 1st & 2nd StrikesBetween 2nd & 3rd StrikesBetween 3rd & 4th StrikesAbove 4th Strike
Delta+ve+ve+ve+ve+ve
Gamma+ve-ve +ve-ve +ve-ve +ve-ve
Theta-ve+ve -ve+ve -ve+ve -ve+ve
Vega+ve-ve +ve-ve +ve-ve +ve-ve

Call Accumulator Expiry Values

Figure 1 and the following illustrations use as the example the Nikkei 225 Index with strikes as per legend. The dots mark settlement values when the Nikkei 225 settles exactly on a strike at expiry.

call accumulator

Fig.1 – Nikkei 225 Binary Options Call Accumulator Price Profile at Expiry

Call Accumulator Over Time

The profiles of Figure 2 show how the binary options call accumulator is affected by the passing of time. Since the strategy is a weighted average of the individual binary call options within the binary options call accumulator the profiles closely map each other until there is only one day or less to expiry. As with the eachway call option this strategy can be made more or less aggressive in terms of delta by the narrowing or broadening of the gap between strikes, plus the incremental increases in settlement price will contribute to the delta profile.

call accumulator

Fig.2 – Nikkei 225 Binary Options Call Accumulator Price Profile w.r.t. Time to Expiry

In the example of Figure 2 at the Nikkei 225 Index price of 8,000 the 25-day binary options call accumulator has a fair value of 3.00. So, with the lowest strike price at 8,250 immediately above which the settlement value is 10, the index only has to rise 250 to generate a profit of 10/3―1=233% at expiry. In contrast the 8,250 binary call option with implied volatility 20%, 25 days to expiry and underlying of 8,000 has fair value of 26.96 which on settling in the money would return a profit of 271%, just 38% more, but without the huge upside potential that the binary options call accumulator still offers.

The binary options call accumulator provides a smooth price profile for the strategy with even only 1-day to expiry. It is only with 0.1-day to expiry that the profile looks remotely like the expiry profile. Subsequently this strategy is a great deal less risky for the market-maker as well as the speculator who buys it out-of-the-money because firstly the delta is not high which means directional risk at the trade’s inception, but furthermore the vega is low as witnessed by Figure 3, and finally at expiry the maximum incremental change is just 30 (above the upper strike) which vastly reduces ‘pin’ risk. With these risks taken out of the equation the market-maker is likely to produce highly competitive, tight bid/ask quotes.

Call Accumulator and Implied Volatility

Figure 3 shows the effect of changes in implied volatility on the binary options call accumulator. Even though the range of implied volatilities is wide the price profiles map each other closely reflecting a very low vega. So, we can conclude that from Figures 2 & 3 this strategy is not designed for use as a theta or vega play.

call accumulator

Fig.3 – Nikkei 225 Binary Options Call Accumulator Price Profile w.r.t. Implied Volatility

Call Accumulator Evaluation

Call Accumulator          =

Payout(K1) x Binary Call(K1) + Payout(K2) x Binary Call(K2)

+ Payout(K3) x Binary Call(K3) + Payout(K4) x Binary Call(K4)

where K1 is the lowest strike, K4 the highest strike, and the Payouts are the incremental increases in settlement price and have to aggregate to 1, e.g. in the above example Payout1 = 10%, Payout2 = 20%, Payout3 = 30% and Payout4 = 40%.

Although in the examples above the strikes are equidistant that also is not cast in stone.

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