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.

Question

Quizplus · Accepted Answer

The delta of a call option in the Black-Scholes model is given by $N(d_1)$, where $N$ is the cumulative distribution function of the standard normal distribution, and $d_1$ is a specific term in the Black-Scholes formula. This represents the rate of change of the option price with respect to changes in the underlying asset price.

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

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