Monte-Carlo

TL;DR for operators A model-risk team estimating failures too rare for ordinary sampling has to decide which kind of error it can least afford. The benchmark shows that this choice can reverse which estimator looks best. Under approximately symmetric penalties, GA-AMLS has much lower average SPB loss than QLD for the 1-layer and 4-layer models. When the loss instead makes underestimation much more costly, QLD sharply outperforms GA-AMLS—even though QLD systematically overestimates and GA-AMLS has lower bias. ...

TL;DR for operators American options are awkward because the model must decide not only what the contract is worth, but also where exercise becomes optimal. That turns pricing into a free-boundary problem, which is exactly the kind of thing that makes high-dimensional PDE methods start sweating through their nice academic shirts. Jasper Rou’s paper extends Time Deep Gradient Flow (TDGF) to American basket put options under multidimensional Black-Scholes and Heston models.1 The useful trick is not “throw a neural network at finance”. We have tried that spell before; it produces PowerPoint before it produces risk control. The actual mechanism is more specific: TDGF trains a neural PDE solver through time steps, only applies the PDE loss in the continuation region, and builds the payoff floor into the network so the model cannot price below the intrinsic value. ...