https://inflection-quant.pages.dev/tags/kurtosis/Recent content in Kurtosis on Inflection Quant LabHugoen-usThu, 16 Apr 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/vol_skewness_kurtosis/Thu, 16 Apr 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/vol_skewness_kurtosis/<h2 id="why-this-matters">Why This Matters</h2> <p>Most of my early intuition about options came from the Black-Scholes model, which is clean and widely used. But once I started working with real option data, it becomes clear that the Black-Scholes assumption of a lognormal distribution is too restrictive. For a given maturity, the implied volatility is not constant across strikes, and its shape suggests asymmetry and heavy tails in the risk-neutral distribution.</p> <p>That leads to a more basic question. Instead of imposing a parametric model and calibrating its parameters, is there a way to extract volatility, skewness, and kurtosis directly from option prices in a model-free way? This is where the Bakshi, Kapadia, and Madan (2003) framework becomes useful. Their key idea is that smooth payoff functions can be represented as a continuum of vanilla options across strikes. In this view, volatility, skewness, and kurtosis are not model assumptions or calibration outputs. They are quantities that can be recovered from market prices through static option replication.</p>