Time-independent pricing of options in range bound markets

Abstract: 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.