Correct answer: C

Asian options are path dependent, so the payoff depends on an average of the underlying price over some period rather than only the terminal price.

• A is true: averaging reduces volatility of the payoff, so Asian options are usually cheaper than vanilla options.
• B is true: geometric averages are mathematically easier to handle than arithmetic averages, so they are easier to price.
• C is false: in practice, most traded Asian options use an arithmetic average, not a geometric average.
• D is true: like lookbacks, Asians depend on the path of the underlying.

Therefore, the exception is C.