TV is a theoretical value of the option according to the
Black-Scholes model, which is calculated on the basis of the average volatility for 10 days on 3 averages (10, 30 and 60 days). It is a kind of benchmark.
Users are free to put a value higher or lower than a TV, though TV is a baseline followed by all traders
Implied volatility
(or IV for short) is an "underlying" volatility, in other words it is
the current market valuation.
The higher it is, the more expensive the option will be.
