New simulation methodology for finance: duality theory and simulation in financial engineering
Proceedings of the 35th conference on Winter simulation: driving innovation
Function-approximation-based importance sampling for pricing American options
WSC '04 Proceedings of the 36th conference on Winter simulation
Function-approximation-based perfect control variates for pricing American options
WSC '05 Proceedings of the 37th conference on Winter simulation
A study of variance reduction techniques for American option pricing
WSC '05 Proceedings of the 37th conference on Winter simulation
Proceedings of the 38th conference on Winter simulation
50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications
Management Science
Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Evaluating Portfolio Policies: A Duality Approach
Operations Research
Monte Carlo simulation in financial engineering
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
An irregular grid approach for pricing high-dimensional American options
Journal of Computational and Applied Mathematics
A New Learning Algorithm for Optimal Stopping
Discrete Event Dynamic Systems
An efficient implementation of a least squares Monte Carlo method for valuing American-style options
International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
On application of nonparametric regression estimation to options pricing
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Information Relaxations and Duality in Stochastic Dynamic Programs
Operations Research
Regression Methods for Stochastic Control Problems and Their Convergence Analysis
SIAM Journal on Control and Optimization
Monte Carlo Bounds for Game Options Including Convertible Bonds
Management Science
Convex Duality in Stochastic Optimization and Mathematical Finance
Mathematics of Operations Research
Dual Valuation and Hedging of Bermudan Options
SIAM Journal on Financial Mathematics
Representations for Optimal Stopping under Dynamic Monetary Utility Functionals
SIAM Journal on Financial Mathematics
Forest of stochastic meshes: A new method for valuing high-dimensional swing options
Operations Research Letters
Primal and Dual Pricing of Multiple Exercise Options in Continuous Time
SIAM Journal on Financial Mathematics
Pathwise Optimization for Optimal Stopping Problems
Management Science
Tight bounds for American options via multilevel Monte Carlo
Proceedings of the Winter Simulation Conference
Pricing American options under partial observation of stochastic volatility
Proceedings of the Winter Simulation Conference
Monte Carlo methods in finance: an introductory tutorial
Proceedings of the Winter Simulation Conference
Pathwise derivative methods on single-asset american option sensitivity estimation
Proceedings of the Winter Simulation Conference
Multivariate convex regression with adaptive partitioning
The Journal of Machine Learning Research
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We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest.