DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models
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.
Related
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BibTeX
@misc{itkin2026dsinc,
title = {{DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models}},
author = {Andrey Itkin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28847},
eprint = {2610.28847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28847},
}
RIS
TY - UNPB
TI - DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models
AU - Andrey Itkin
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28847
UR - https://arxiv.org/abs/2610.28847
AB - 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.
ER -