Monte Carlo Methods for Pricing American Options: Developments and Limits
Summary
The document asks what changed in Monte Carlo methods for pricing American options between 2005 and 2016, following earlier machine-learning work on optimal stopping. One answer argues that the period brought few groundbreaking Monte Carlo advances and that finite-difference and finite-element methods were often favored for speed, robustness, and better Greek estimates. It identifies adjoint algorithmic differentiation combined with Monte Carlo as an effort to address unstable sensitivities, and multilevel Monte Carlo as another area to investigate.
A second answer claims progress around Longstaff-Schwartz regression, parallel and high-performance computing, adaptive methods, machine learning, and numerical integration. It does not cite specific studies or offer evidence to support those claims, so they should be treated as broad leads rather than a verified literature review. The thread gives no benchmark results, implementation details, or systematic comparison of methods; readers seeking a research survey would need to consult the suggested literature and evaluate each method’s accuracy, computational cost, and Greek stability.
Key ideas
- Longstaff-Schwartz estimates continuation values through regression in a Monte Carlo framework.
- One response characterizes major Monte Carlo breakthroughs in the period as limited.
- Finite-difference and finite-element approaches are presented as alternatives with potential speed and Greek advantages.
- Adjoint algorithmic differentiation with Monte Carlo is mentioned as a way to address sensitivity instability.
- Multilevel Monte Carlo is identified as another relevant development, while broad progress claims lack supporting citations.
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Full text
# Recent developments in American options # Recent developments in American options I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based on Monte Carlo) I appreciate it if you can offer me some clues! ## Answer by KT8 (score 2) https://quant.stackexchange.com/a/82208 I don't think that there have been much development in the American-option field in MC methods. I think the field realised that the way to go are FDM and FEM. This methods are fast, robust, and lead to better greeks, so MC techniques lost most momentum here. You may find some info here in this medium post and here in another post from this forum. By "not much" on the top comment I refer to groundbreaking delevopments. Something has been done in the area by trying to integrate AAD together with MC (this would try to solve the unstable greeks problem), see this paper for example. Other developments I could point to are multilevel MC methods, on which M. Giles has some notes/books, for example this book. If someone else knows about some recent papers I'd also be interested actually. ## Answer by AshaKantaSharma (score -3) https://quant.stackexchange.com/a/80230 The literature on the pricing of American options has seen a great advancement between the year 2005 and 2016 with focus on the Monte Carlo estimated price. Some of the notable emerging methods include the Longstaff-Schwartz Algorithm which estimates the option’s continuation value through regression. Scientists have fine-tuned and advanced the circumstances for the algorithm using parallel computing, adaptive structures, high-performance computing, machine learning methods, combined methods, and better numerical integration alongside optimization circumstances. Developments in the previous couple of years have also seen different researchers and authors discussing the American option pricing in regard to its troubles in different academic journals and conference papers.
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