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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Definitions:

Equilibrium Reaction

A reversible chemical reaction where the rate of the forward reaction equals the rate of the backward reaction, resulting in stable concentrations of reactants and products.

Activation Energy Barrier

The minimum amount of energy required to initiate a chemical reaction.

Collision Theory

A theory that explains how chemical reactions occur and why rates of reactions vary for different reactions.

Forward Reaction

A chemical reaction where reactants convert into products, typically highlighted in a chemistry equilibrium context.