easy · Quantitative Finance derivatives

When pricing a 'Digital' (or Binary) call option near expiry with the spot price very close to the strike, why does delta-hedging become effectively impossible?

1. The Vega becomes negative, meaning volatility increases decrease the option's value.
2. Put-Call parity is violated for digital options, making replication impossible.
3. The Gamma becomes zero, making the hedge too static to capture moves.
4. The Delta spikes toward infinity as the payoff approaches a step function.

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