DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models

Paper: arXiv 2610.28847

Authors: Andrey Itkin

Abstract

This paper extends the damped-sinc (DSINC) method for American options beyond the affine Heston class to general one-factor stochastic-volatility models. We show that the collapse identity, which reduces the early-exercise integral to a single spectral integral, remains valid for these models. Damping between zero and one is admissible whenever the discounted spot is a nonnegative local martingale. An Itô transformation of the volatility factorizes the conditional characteristic function and identifies a natural coordinate for approximating the exercise boundary. The 3/2 model admits closed-form joint transforms in terms of Kummer functions, while uncorrelated SABR admits a Bessel representation. When a practical closed-form transform is unavailable, the required volatility integral is computed directly by solving one backward equation per frequency, without a grid in the log-price. Through a known change of volatility coordinate, this approach also accommodates correlated SABR. Tests on the 3/2, SABR, GARCH and lognormal-volatility models show agreement with fine finite-difference benchmarks to within one basis point of the strike. Computational cost is comparable to or lower than that of our finite-difference implementation, except for the slower Hankel implementation of uncorrelated SABR.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical extension of the DSINC method to non-affine stochastic volatility models, demonstrating significant theoretical depth. It includes empirical tests against finite-difference benchmarks, showing strong agreement and practical applicability. The approach is novel in its generalization of the collapse identity and handling of various non-affine models.

Research Flowchart

  flowchart TD
    A[Research Goal: Extend DSINC for American Options to General Stochastic-Volatility Models] --> B{Methodology: Damped-Sinc (DSINC) beyond Heston};
    B --> C{Key Concepts: Collapse Identity, Itô Transformation, Natural Coordinate for Exercise Boundary};
    C --> D[Models Tested/Inputs: 3/2, SABR (Uncorrelated/Correlated), GARCH, Lognormal-Volatility Models];
    D --> E{Computational Processes: Closed-form Transforms (Kummer, Bessel), Backward Equation for Volatility Integral};
    E --> F[Key Findings: Collapse Identity Valid; Agreement with Benchmarks (1 BPS); Efficient Computation];