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

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 It\^o 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.