arXiv subjects

Liming Feng

Publications and source records attributed to Liming Feng.

3 recordsLinked to original sources

arXiv2026

Arbitrage-Free Multi-Maturity Risk-Neutral Marginals

Many quantitative finance methods and applications are formulated in terms of option-implied risk-neutral marginals rather than directly in terms of option prices. Representative examples include martingale optimal transport, Bass local-volatility calibration, scenario analysis, and option-implied tail-risk measurement. The desired risk-neutral marginals should define a genuine probability law on the entire support, reproduce the input arbitrage-free option prices exactly, be free of butterfly and calendar arbitrage, and admit efficient evaluation of the density, distribution function, and quantiles, as well as Monte Carlo sampling. Existing methods typically optimize only a subset of these properties, depending on their intended purpose. This leaves a gap between upstream arbitrage-free option prices and the readily usable risk-neutral marginals required by downstream applications. We propose an explicit construction of risk-neutral marginals from discrete arbitrage-free option prices. On the observed strike range, probability mass is assigned interval by interval to exactly reproduce the input option prices. Outside the observed range, closed-form power-law tails complete the distribution by satisfying price and slope boundary conditions and allocating the remaining probability mass. Butterfly- and calendar-arbitrage-freeness are guaranteed by construction. The construction is feasible by design and computationally efficient. The resulting marginal laws admit closed-form densities, distribution functions, quantiles, and efficient Monte Carlo sampling. Numerical experiments on synthetic SSVI data and S\&P~500 market data demonstrate that the proposed construction efficiently and robustly produces marginals satisfying all of these properties in practice.

q-fin.CP↗

arXiv2025

Volatility Calibration via Automatic Local Regression

Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices across all strikes and maturities with high accuracy. However, LV calibration is fundamentally ill-posed: finite market observables must determine a continuously-defined surface with infinite local volatility parameters. This ill-posed nature often causes spiky LV surfaces that are particularly problematic for finite-difference-based valuation, and induces high-frequency oscillations in solutions, thus leading to unstable Greeks. To address this challenge, we propose a pre-calibration smoothing method that can be integrated seamlessly into any LV calibration workflow. Our method pre-processes market observables using local regression that automatically minimizes asymptotic conditional mean squared error to generate denoised inputs for subsequent LV calibration. Numerical experiments demonstrate that the proposed pre-calibration smoothing yields significantly smoother LV surfaces and greatly improves Greek stability for exotic options with negligible additional computational cost, while preserving the LV model's ability to fit market observables with high fidelity.

q-fin.CP↗

arXiv2024

Robust and Fast Bass Local Volatility

The Bass Local Volatility Model, as studied in {henry2021bass}, stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional local volatility models. However, its performance highly depends on accurate construction of risk neutral densities and the corresponding marginal distributions and efficient numerical convolutions which are necessary when solving the associated fixed point problems. In this paper, we propose a new approach combining local quadratic estimation and lognormal mixture tails for the construction of risk neutral densities. We investigate computational efficiency of trapezoidal rule based schemes for numerical convolutions and show that they outperform commonly used Gauss-Hermite quadrature. We demonstrate the performance of the proposed method, both in standard option pricing models, as well as through a detailed market case study.

q-fin.CP↗