The correct answer is A. frankness.
Perspicuity is the quality of being clear and easy to understand. Frankness is the quality of being honest and direct. Bluntness is the quality of being direct and to the point, sometimes to the point of being rude. Obtuseness is the quality of being slow to understand or respond. Vivacity is the quality of being lively and full of energy.
In this case, the author is being frank in his style. He is being honest and direct in his writing, and he is not trying to hide anything from the reader. He is also being clear and easy to understand, which makes his writing perspicuous.
The other options are not as accurate descriptions of the author’s style. Bluntness could be a possible description, but it is not as accurate as frankness. Obtuseness is not a good description at all, because the author is not slow to understand or respond. Vivacity is also not a good description, because the author’s writing is not lively or full of energy.