# Binary Options Call Delta

# Binary Options Call Delta definition and profiles

This post ist published by Hamish Raw of https://hamishraw.com/

Binary call options delta is the first derivative of the option price w.r.t. a change in the underlying price. In effect the binary call options delta is the gradient of the price profile of the binary call option.

The delta, whether it is of the binary call option, conventional put option or any kind of exotic option, provides an instant equivalent position in the underlying, e.g. if the delta is 0.30 and the option has the same tick value as, say, an underlying future then a long 100 call position would be equivalent at that point to being long 100 x 0.30 = 30 futures. This ‘greek’ therefore is critical in the hedging of an options portfolio against an adverse movement in the underlying price.

Fig.1 illustrates the $100 oil binary call options delta against days to expiry. What may come as a surprise to conventional options practitioners is the fact that the binary options call delta is at its highest when at-the-money.

Although the scale might suggest that the binary call options delta remains fairly low, this would be a grave mistake since the delta of the at-the-money tends to infinity as time to expiry approaches zero. The 8-day profile remains at a very low level with a maximum value of just 0.0898 when at-the-money. What starts off as a placid instrument turns into an unmanageable monster over the last few hours of its life as the at-the-money delta becomes so high that the option becomes unhedgeable. In fact with 0.001 days to expiry (1.44mins) the at-the-money binary call options delta has risen to 8.03. These deltas would be hugely increased should the contract be less volatile than oil, say a government bond, so that with 5.0% implied volatility and 2hrs 24 mins to expiry the delta would be 4.82 and rising.

Fig.2 shows various binary call options deltas with 5 days to expiry where the delta remains extremely manageable.

The greater premium of the 5 day binary call option means that the gradient of the price profile of the binary call option remains shallow; in effect no one is going to get rich or poor trading a 5 day binary call with implied volatility at 30%, the gearing is just not available.

Those familiar with the conventional greeks will be aware that the gamma is the first derivative of the delta, and that the gamma of a conventional option is always positive. Check out the above profiles, not here they are! Binary call option gamma yet again does not follow conventional rules…….

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