A put option can be replicated by holding a position in stock and bonds, i.e., $P = B + \Delta S$ where $\Delta$ is the delta of the put option. Comparing the replication formula to the Black-Scholes formula, and assuming no dividends, 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 equal to $N \left( - d _ { 1 } \right)$ .
D) The delta is the long position in stock needed to replicate the option.

Question

Quizplus · Accepted Answer

DThe delta of a put option according to the Black-Scholes model is $N(-d_1)$, where $N(\cdot)$ is the cumulative distribution function of the standard normal distribution. This represents the sensitivity of the option's price to a small change in the stock price. Additionally, the delta can be interpreted as the equivalent position in the stock needed to replicate the option's payoff, hence both C and D are correct.

A Put Option Can Be Replicated by Holding a Position P=B+ΔSP = B + \Delta SP=B+ΔS

A Put Option Can Be Replicated by Holding a Position $P = B + \Delta S$