A call option in the Black-Scholes model is a function of the stock price and time, i.e., $C ( S , t )$ . Which of the following statements is valid with regards to the change in the option price over time, i.e., $d C ( S , t )$ ?
A) The expected change $E ( d C )$ is not a function of stock volatility-taking expectations eliminates the Wiener process term.
B) The expected change over time is not a function of the remaining maturity of the option, only of the amount of time over which the change is examined.
C) The expected change in the call price is not a function of the risk-free interest rate but only the growth rate of the stock at the specific point in time.
D) None of the above.

Question

Quizplus · Accepted Answer

The Black-Scholes model shows that the expected change in the option price over time is indeed affected by stock volatility, the remaining maturity of the option, and the risk-free interest rate, contrary to the statements made in options A, B, and C.

A Call Option in the Black-Scholes Model Is a Function C(S,t)C ( S , t )C(S,t)

A Call Option in the Black-Scholes Model Is a Function $C ( S , t )$