Extending DSINC beyond Heston to Non-Affine Stochastic-Volatility Models

01 ABSTRACT

The paper proves that the collapse identity underlying the DSINC method remains valid for general one-factor stochastic-volatility models, reducing the early-exercise integral to a single spectral integral. The author tests the approach on the 3/2, SABR, GARCH, and lognormal-volatility models, finding agreement with fine finite-difference benchmarks to within one basis point of the strike. The author's view is that computational cost is comparable to or lower than finite differences, except for the slower Hankel implementation of uncorrelated SABR.

02 KEY FINDINGS

1. The collapse identity remains valid for non-affine one-factor stochastic-volatility models; damping between zero and one is admissible when the discounted spot is a nonnegative local martingale.
2. An Itô transformation of the volatility factor factorizes the conditional characteristic function and identifies a natural coordinate for approximating the exercise boundary; the 3/2 model admits closed-form joint transforms via Kummer functions, and uncorrelated SABR admits a Bessel representation.
3. When a practical closed-form transform is unavailable, the volatility integral is computed by solving one backward equation per frequency without a grid in the log-price; tests show accuracy within one basis point and cost comparable to or lower than finite differences.