Valuing American Options by Simulation: A Simple Least-Squares Approach

By Francis A. Longstaff, Eduardo S. Schwartz. 2001

3,451 citations recorded by the source corpus.

Subfields: Finance, Strategy and Management

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Citations in the corpus

Stochastic Primal-Dual Q-Learning (2018, neutral): “The problem of learning a map from world observations to actions, called a policy, lies at the core of many sequential decision problems, such as robotics (Chen et al., 2017), artiﬁcial intelligence (Mnih et al., 2015), ﬁnance (Longstaﬀ and Schwartz, 2001), and economics (Tesauro and Kephart, 2002).”
DGM: A deep learning algorithm for solving partial differential equations (2017, positive): “[32] developed an algorithm for the solution of a discrete-time version of a class of free boundary PDEs.”
Pricing American Options: A Duality Approach (2018, methodology): “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.”
Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule (2003, methodology): “Longstaff and Schwartz (2001) generate 8 different random stock price paths in order to apply MonteCarlo to price this put option.”
Stochastic Primal-Dual Q-Learning Algorithm For Discounted MDPs (2019, background): “The problem of learning a map from world observations to actions, called a policy, lies at the core of many sequential decision problems, such as robotics [1], artificial intelligence [2], finance [3], and economics [4].”
MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE‐EXERCISE OPTIONS (2004, positive): “We employ value-function regression, in particular the method by Longstaff and Schwartz [9] to obtain an approximation to the marginal value function.”
Valuation of large variable annuity portfolios under nested simulation: A functional data approach (2015, methodology): “Another approach involves a statisticalmodel that regresses the liability value on some key economic factors (Cathcart and Morrison, 2009) and the least-square Monte Carlo method (Carriere, 1996; Longstaff and Schwartz, 2001) is used to approximate the future liabilities at each time step.”
The Linear Programming Approach to Approximate Dynamic Programming (2003, background): “Outline Markov decision processes Approximate Dynamic Programming Approximate linear programming Performance and Error Analysis Constraint Sampling http://www.mit.edu/∼pucci – p. 2/29”
Option Pricing Under a Double Exponential Jump Diffusion Model (2004, background): “For example, Merton (1974), Black and Cox (1976), and more recently Leland (1994), Longstaff (1995), Longstaff and Schwartz (1995), among others, use lookback and barrier options to value debt and contingent”
TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON‐NESTED MONTE CARLO (2009, methodology): “Next we approximate Z ti by simulation based least squares regression on basis functions as was suggested by Longstaff and Schwartz (2001) for lower”
Monte Carlo valuation of American options (2002, neutral): “…of an American option, and in Section 4 we take this further with a numerical study of some examples: the standard American put; an American min-put (see Hartley 2000); a Bermudan max-call (see Broadie and Glasserman 1997b); and an American–Bermudan–Asian example of Longstaff and Schwartz (2001).”
PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES (2004, neutral): “[36], [32], [25], [23], [27], [16] and the bibliography therein.”
Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2005, methodology): “We refer to Carrière [11], Longstaff and Schwartz [35], Lions and Regnier [33], Bally and Pagès [3], Glasserman [26], and Bouchard and Touzi [9].”
A simple approach for pricing equity options with Markov switching state variables (2006, background): “Longstaff and Schwartz ( 2001 ) provide a simulation model in which American options may be valued quite easily; their approach would be applicable to the problem we address in this paper.”
A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS (2005, methodology): “The algorithm devised by Longstaff and Schwartz (2001) is based on conditional expectation approximation by regression on a finite subfamily (ϕi(St))i∈I of a basis (ϕk(St))k≥1 of L2(σ (St), P).”