hard · FRM Part 1 Valuation and Risk Models
A binary 'cash-or-nothing' call option pays 50 if the stock price is above $100 at expiry.
As the option approaches expiry with the stock price very close to $100, what happens to the option's Delta?
- Delta becomes extremely large and unstable (explosive), creating significant hedging challenges.
- Delta decays gradually to zero as the option's remaining time value erodes toward expiry.
- Delta stabilizes near a value of 0.50 close to expiry, regardless of the realized volatility.
- Delta stays constant throughout, since the fixed $50 cash payoff amount never itself changes near expiry.
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