🤖 AI Summary
This study addresses the challenge of simultaneously achieving precise local shape control and strict static no-arbitrage compliance in implied volatility curve modeling. To this end, it proposes a parsimonious and interpretable parametric approach grounded in the risk-neutral distribution. By introducing parameters that exhibit stable cross-maturity patterns, the method directly governs local curvature characteristics—such as convexity and concavity—while inherently satisfying no-arbitrage constraints. The resulting model flexibly accommodates diverse curvature patterns and supports both term structure interpolation and dynamic modeling. Empirical validation on a two-year dataset of S&P 500 options, encompassing over 250,000 calibrated volatility curves, demonstrates the stability, generalizability, and high fidelity of the proposed parameterization in capturing complex market dynamics.
📝 Abstract
We present a distinctive approach to parameterizing the risk neutral distribution. Using parsimonious and interpretable parameters, the model provides direct and localized control over the shape of the implied volatility curve. It captures a wide variety of shapes, including those with local concavity. Empirical results demonstrate accurate calibration across a quarter million curves from a two-year Standard and Poor's 500 index option dataset. The fitted parameters exhibit stable patterns across tenors, enabling term structure interpolation and dynamic process construction without static arbitrage.