A Call Option Can Be Replicated by Holding a Position $C = \Delta S - \bar { B }$

question 22

Multiple Choice

A call option can be replicated by holding a position in stock and shorting bonds, i.e., $C = \Delta S - \bar { B }$ where $\Delta$ is the delta of the call option. Comparing the replication formula to the Black-Scholes formula (assume a non-dividend-paying stock) , what can you say about the delta of the option?

• A) The delta is equal to the probability that the option will end up in the money.
• B) The delta is equal to \(N \left( d _ { 1 } \right)\) .
• C) The delta is the short position in stock needed to replicate the option.
• D) There is insufficient information to say anything about the delta.

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