First step in attempting to find the probability of the penetration out of support/resistance levels is to consider a separation of variables in Black-Scholes valuation formula. The separation of variables is possible due to the stationary price moving in the region bounded by support and resistance levels.
having a strike price of 2,50 USD , the market price at 2,40 USD give a of , say 130%. To take the example to the extreme, a strike price of 7,40 USD for the same market price, have of 285%. It is easy to see that option value in the last case will decay more rapidly than in the first case.
The probability of the particle tunneling out of the box – also called transmission coefficient- is becoming, in the case of stock market, the probability of stock price to penetrate out of the support and resistance region.
Choosing an option contract having the strike price as nearest as possible to resistance or support, it can be noticed that transmission coefficient is depending only on interest rate, volatility and strike price of the underlying stock.
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