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In financial mathematics, the martingale property often serves as an essential foundation for the stochastic processes that underlie securities pricing models. According to martingale theory, the most accurate predictor for a security's future price, given all available past and current information, is the current price. However, it is conceivable that a stochastic process with a martingale property could still generate real, observable support and resistance levels for a security's price.

I am not interested in trading strategies that attempt to capitalize on support/resistance phenomena. Instead, my focus is on empirical research that explores the existence of genuine support and resistance levels within martingale processes for security pricing.

The reason this inquiry is significant is that it potentially challenges the commonly accepted notion that option volatility surfaces should be smooth and free of discontinuities or "kinks." If genuine support and resistance levels were to exist within an efficient market framework, it would stand to reason that the option volatility surface might display "kinks" at strike prices corresponding to these support and resistance levels.

Is there any empirical research that investigates the existence of such support and resistance levels within martingale price processes for securities, and its consequential impact on the smoothness or kinkiness of the option volatility surface?

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