  Assuming that price of the underlying stock is moving in range bound, the
Black-Scholes formula for options pricing supports a separation of variables.
The resulting time-independent equation is solved employing different behavior
of the option price function and three significant results are deduced. The
first is the probability of stock price penetration through support or
resistance level, called transmission coefficient. The second is the distance
that price will go through once stock price penetrates out of the range bound.
The last one is a predicted short time dramatic fall in the stock volatility
right ahead of price tunneling. All three results are useful tools that give
market practitioners valuable insights in choosing the right time to get
involved in an option contract, about how far the price will go in case of a
breakout, and how to correctly interpret volatility downfalls.
