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

By Andrey Itkin

Rating

1795
Battle Count: 50

Relevance

8/10
Highly relevant for quantitative researchers and traders dealing with exotic or American options in equity and FX markets. The ability to price American options under realistic non-affine volatility dynamics (like 3/2 or SABR) accurately and efficiently is crucial for hedging and valuation.

Implementation Complexity

9/10
High complexity. Requires deep understanding of stochastic calculus (Itô transformations, bridge functionals), special functions (Kummer, Bessel), and numerical linear algebra (matrix exponentials, Krylov subspace methods). Implementing the fixed-frequency solver and handling the damping conditions correctly is non-trivial.

Reproducibility

3/5
The paper provides detailed mathematical derivations, algorithmic steps, and specific parameter settings for all numerical tests. However, no public code repository URL is provided in the text. The method relies on standard libraries (NumPy, SciPy) and well-defined mathematical functions (Kummer, Bessel), making it reproducible for an expert with the provided formulas.

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.

Links

arXiv:2610.28847 · Paper rankings

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