I'll venmo a grand to anyone who gets it right (wrong with BSM/traditional OPM). There is only one correct answer. I am going to email it to myself right now!
Well, there are two issues with BSM, etc. The one I emailed to myself and the other is the switch values relating to earnings releases and known macro events.
Using MAD instead of StDev ? Mean Absolute Deviation Code: # Step 1: Compute the mean return mean_return = returns.mean() # Step 2: Compute Mean Absolute Deviation mad = (returns - mean_return).abs().mean() # Step 3: Annualize the MAD (if using daily returns) annualized_mad = mad * np.sqrt(252)
are you being serious.. Argument for Polarized Fractal Efficiency (PFE) Over Standardized Volatility Measurements Polarized Fractal Efficiency (PFE) offers a superior approach to measuring market volatility compared to standardized volatility metrics, such as standard deviation, Average True Range (ATR), or open-to-close price changes. Traditional volatility measurements, while widely used, fail to capture the intricate, non-linear dynamics of price movements driven by market participant behavior. PFE addresses these shortcomings by quantifying the cumulative, fractal-like path of price action, providing a more accurate and comprehensive assessment of true market volatility. This argument outlines the key reasons why PFE is a more effective volatility metric, emphasizing its ability to reflect the complex, erratic nature of price fluctuations that standardized methods overlook. Standardized volatility measurements primarily focus on linear or aggregated price changes, such as the dispersion of prices around a mean (standard deviation) or the range between high and low prices (ATR). These methods oversimplify market dynamics by prioritizing net price movements or coarse price ranges, often ignoring the rapid, oscillatory price shifts that characterize active trading periods. For instance, a session with significant intraday price swings but a minimal net change may be undervalued, despite reflecting intense participant activity. This linear bias fails to account for the fractal nature of price paths, where small-scale reversals, consolidations, and directional changes contribute substantially to the market’s volatility. Consequently, standardized metrics can misrepresent the true intensity of market conditions, leading to suboptimal trading decisions. In contrast, PFE measures the total distance traveled by price through its cumulative, absolute price changes across all increments within a given period. By summing these micro-movements, PFE captures the full spectrum of price action, including abrupt reversals and erratic fluctuations that standardized metrics disregard. This fractal approach aligns with the chaotic, participant-driven nature of markets, where volatility is not merely a function of endpoint differences but of the entire price trajectory. PFE’s emphasis on polarization—highlighting the directional intensity or clustering of price swings—further enhances its precision, as it weights significant movements to reflect heightened market activity. This ensures a more nuanced representation of volatility, particularly in periods of high-frequency trading or choppy conditions. Moreover, PFE incorporates an efficiency component, normalizing the fractal path against the straight-line price change to create a ratio that quantifies the complexity of price movements relative to their net effect. This efficiency ratio provides a standardized measure that is comparable across different market conditions, unlike traditional volatility metrics that can be skewed by large, unidirectional moves. By focusing on the structural intricacy of price paths, PFE avoids the pitfalls of time-based biases inherent in standardized methods, making it particularly suitable for environments where price movement patterns are prioritized. This normalization ensures that PFE remains a robust and adaptable metric, capable of reflecting volatility in both trending and ranging markets. In conclusion, Polarized Fractal Efficiency surpasses standardized volatility measurements by offering a more accurate, comprehensive, and structurally relevant assessment of market volatility. Its ability to capture the fractal, polarized nature of price movements addresses the limitations of linear, aggregated metrics, providing traders with a clearer understanding of market dynamics. By prioritizing the cumulative path and efficiency of price action, PFE delivers a superior volatility gauge that enhances decision-making in dynamic trading environments, ensuring a more precise alignment with the true behavior of market participants. The Polarized Fractal Efficiency (PFE) is a volatility measure that quantifies the cumulative, fractal-like path of price movements, capturing the intricate, non-linear dynamics of market participant behavior more effectively than standardized volatility metrics. As you’ve emphasized, PFE focuses on the total "distance" traveled by price, including all micro-movements, reversals, and fluctuations, rather than just net price changes or high-low ranges. Below, I’ll provide the basic mathematical formula for PFE in a clear, concise manner, avoiding examples, code, specific numbers, or references to your trading systems (e.g., spatial velocity, tick-based charts), as requested. The explanation will remain professional and focused solely on the formula, ensuring it’s accessible and directly addresses your query. Basic PFE Formula The PFE formula measures the efficiency of price movements by comparing the total fractal path (the sum of absolute price changes) to the straight-line distance (the net price change) over a given period, often normalized to provide a standardized metric. The basic mathematical formula for PFE is: PFE = (sqrt(sum((P_(i+1) - P_i)^2)) / sum(|P_(i+1) - P_i|)) * sign(P_n - P_1) Where: P_i: Price at point i. n: Number of price points. sum(|P_(i+1) - P_i|): Total fractal path (sum of absolute price changes). sqrt(sum((P_(i+1) - P_i)^2)): Straight-line distance. sign(P_n - P_1): +1 for upward net change, -1 for downward. Explanation of the Formula Fractal Path: The denominator (∑∣Pi+1−Pi∣ \sum |P_{i+1} - P_i| ∑∣Pi+1−Pi∣) sums the absolute price changes, capturing every price movement, including reversals and oscillations, akin to walking the jagged “coastline” of price action. Straight-Line Distance: The numerator (∑(Pi+1−Pi)2 \sqrt{\sum (P_{i+1} - P_i)^2} ∑(Pi+1−Pi)2) calculates the Euclidean distance, representing the direct path from the start to end price, like a crow flying a straight line. Efficiency Ratio: The ratio compares the straight-line path to the fractal path, with a lower ratio indicating a more complex, volatile path (high volatility) and a higher ratio indicating a direct, trending path (low volatility). Polarization: The sign term preserves the direction of the net price move, ensuring PFE reflects whether the market’s volatility is bullish or bearish. This formula provides a normalized measure of volatility, emphasizing the fractal complexity and directional intensity of price movements, making PFE a more accurate gauge than standard metrics.