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