Answer: The historical volatility, as in input into Black-Scholes-Merton, tends to converge on implied volatility as the option is nearer to being “at the money” (ATM)

**Correct answer: B** Option value is generally an increasing function of volatility for both calls and puts, and this remains true for both American and European options. So **C** and **D** are true. Also, when volatility is set to zero in the Black-Scholes-Merton framework, the European call value collapses to its lower bound under the usual no-dividend assumptions, so **A** is true. The false statement is **B** because **historical volatility** and **implied volatility** are different concepts: - **Historical volatility** is measured from past price data. - **Implied volatility** is backed out from current market prices. Being near-the-money does not make historical volatility “converge” to implied volatility. At-the-money options are simply the most sensitive to volatility changes (high vega), not a place where the two volatility measures become the same.

Author: Manit Arora