Explanation:
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:
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.
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Question-179.3. EACH of the following is true about option volatility EXCEPT:
A
The lower bound for a European call option is equal to the Black-Scholes-Merton option value where the volatility input is zero
B
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)
C
Option value is an increasing function with volatility for an American or European CALL on a both a dividend- or non-dividend-paying stock
D
Option value is an increasing function with volatility for an American or European PUT on a both a dividend- or non-dividend-paying stock