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Leif Andersen, Andrey Itkin, Rakhymzhan Kazbek · 2026-06-25
The paper develops a faster, more accurate way to price flexible forward FX contracts (where you lock a rate but choose the delivery date within a window) and American options, using a time-varying Heston volatility model. It builds the valuation on an integral equation for the early-exercise boundary and solves it with two spectral methods (COS and a new damped-Sinc scheme), finding DSINC is roughly 12x more accurate than COS and both are about 10x faster than a fine finite-difference solver.
Why it matters: Practitioners pricing or hedging FX flexible forwards and American-style options may value methods that respect the volatility skew and its term structure while running in 1-2 seconds. The finding that the early-exercise boundary is strongly nonlinear in variance suggests common simplified approximations could misprice timing optionality.
⚠ This is a computational pricing-methodology result validated against numerical benchmarks, not a trading strategy, and its usefulness depends on the chosen model being an accurate fit to real market dynamics.
A flexible forward (FF) is a customized FX hedging instrument that guarantees a fixed exchange rate while letting the holder choose the delivery date within a pre-agreed window. It is therefore an American-style option on timing, and its valuation must respect the volatility skew of the underlying currency pair. We price FF contracts (and, more generally, American options) under a time-inhomogeneous Heston model which captures the forward-skew term structure while preserving analytical tractability through a recursive (matrix) Riccati solution for the joint characteristic function. Extending the integral-equation (decomposition) approach to time-dependent coefficients, we derive a Volterra equation characterizing the early-exercise surface. The expectation in the decomposition formula is evaluated by two complementary spectral methods: a double cosine (COS) expansion of the transition density, and a damped-Sinc (DSINC) local-basis scheme that is more accurate and stays robust when a low Feller ratio or large vol-of-vol induces Gibbs oscillations in the COS series. Benchmarked against a penalty-iteration MCS-ADI finite-difference solver, both methods price a contract in about 1-2 seconds, roughly an order of magnitude faster than the finest finite-difference grid, while DSINC improves median accuracy over COS by about a factor of twelve. The experiments also show that the early-exercise surface is a substantially nonlinear function of the variance, contrary to the linear-in-variance approximation common in earlier work.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.