medium · Quantitative Finance derivatives
An equity desk is hedging a 'binary' (digital) option that pays $1 if the stock is above the strike at expiry.
As the option approaches expiry and the stock is very near the strike, what is the primary risk-management challenge?
- Delta and gamma become unboundedly large, making the hedge unstable.
- Vega becomes zero, meaning volatility moves no longer affect the price.
- Theta becomes positive, causing the option to gain value as time passes.
- The option price becomes fixed at $0.50, regardless of stock moves.
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