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Well if you think that this model represents reality more accurately than the Black-Scholes assumptions. A lot of people do indeed think so. But I wouldn't say you're "tweaking" Black-Scholes... you're just assuming another model altogether and you will use risk-neutral pricing to compute the fair value of the option at time $t$, just like BS. Frankly, I'm ...
Actually BS model is still applicable in the market where the upwards/downwards move is much more probable than move in the opposite direction. The Black-Scholes price process model has the form: $\frac{dS}{S} = \mu dt + \sigma dW$ And with significantly non-zero $\mu$ (called drift) it will capture just what you are talking about. Quite surprisingly, the ...