It's possible to receive a short explanation what the intention of dual delta ,delta=0.496 ,dual delta=-469? thanks

I've never heard of dual delta. But I'll hazard a guess. Delta is sometimes defined as how much the value of an option will change with a one-point move in the underlying. But if the underlying goes up a point, the option will change in value a different amount than if the underlying goes down a point. Perhaps this is what they mean by dual delta. Two numbers - one the amount the option changes when the underlying goes up a point, the other the amount the option changes when the underlying goes down a point. Like I said, just a guess. It fits the fact that these are two almost-identical deltas, one positive and one negative.

Dual delta is defined as derivative (rate of change) of price with respect to strike. For example CME front month 320 call has mid-market of 17.50 and 330 at 11.80 Dual Delta = (11.80-17.50)/(330-320) = -0.57 For most models like black-scholes & heston type models the relationship between delta and dual delta is trivial: Delta = 1/StockPrice * ( OptionPrice - Strike * DualDelta )