Heston Model

Financial engineers have long sought to tame the volatility surface. From Black-Scholes to Heston, modelers have used parametric tricks to approximate implied volatilities across strikes and maturities. But what happens when the surface refuses to play along—when volatility is rough, the market isn’t Heston, and no closed-form expansion suffices? In today’s article, we explore a signature-based approach from rough path theory that aims to solve this exact problem. The method not only matches the performance of classical asymptotic expansions in well-behaved markets, but even excels when things get bumpy. ...

Pricing American options has long been the Achilles’ heel of quantitative finance, particularly in high dimensions. Unlike European options, American-style derivatives introduce a free-boundary problem due to their early exercise feature, making analytical solutions elusive and most numerical methods inefficient beyond two or three assets. But a recent paper by Jasper Rou introduces a promising technique — the Time Deep Gradient Flow (TDGF) — that sidesteps several of these barriers with a fresh take on deep learning design, optimization, and sampling. ...