Don't fall into the trap of viewing the numbers that Black-Scholes spits out as being "accurate". All of these models are just that: models. They aren't reality but convenient fictions created to try to understand the markets. Price, volume, statistical volatility, interest rates can all be directly measured - they're real. But figures like implied volatility are *implied* i.e. not a directly measurable quantity.
Don't get hung up on being as precise or accurate as possible.
Don't get hung up on being as precise or accurate as possible.