The Experts below are selected from a list of 11775 Experts worldwide ranked by ideXlab platform
Vadim Linetsky - One of the best experts on this subject based on the ideXlab platform.
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optimal stopping and early exercise an eigenfunction expansion approach
Operations Research, 2013Co-Authors: Vadim LinetskyAbstract:This paper proposes a new approach to solve finite-horizon optimal stopping problems for a class of Markov processes that includes one-dimensional diffusions, birth–death processes, and jump diffusions and continuous-time Markov chains obtained by time-changing diffusions and birth-and-death processes with Levy subordinators. When the Expectation Operator has a purely discrete spectrum in the Hilbert space of square-integrable payoffs, the value function of a discrete optimal stopping problem has an expansion in the eigenfunctions of the Expectation Operator. The Bellman's dynamic programming for the value function then reduces to an explicit recursion for the expansion coefficients. The value function of the continuous optimal stopping problem is then obtained by extrapolating the value function of the discrete problem to the limit via Richardson extrapolation. To illustrate the method, the paper develops two applications: American-style commodity futures options and Bermudan-style abandonment and capaci...
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optimal stopping and early exercise an eigenfunction expansion approach
Social Science Research Network, 2013Co-Authors: Vadim LinetskyAbstract:This paper proposes a new approach to solve finite-horizon optimal stopping problems for a class of Markov processes that includes one-dimensional diffusions, birth-and-death (BD) processes, and jump-diffusions and continuous-time Markov chains obtained by time changing diffusions and BD processes with Levy subordinators. When the Expectation Operator has a purely discrete spectrum in the Hilbert space of square-integrable payoffs, the value function of a discrete optimal stopping problem has an expansion in the eigenfunctions of the Expectation Operator. The Bellman's dynamic programming for the value function then reduces to an explicit recursion for the expansion coefficients. The value function of the continuous optimal stopping problem is then obtained by extrapolating the value function of the discrete problem to the limit via Richardson extrapolation. To illustrate the method, the paper develops two applications: American-style commodity futures options and Bermudan-style abandonment and capacity expansion options in commodity extraction projects under the subordinate Ornstein-Uhlenbeck model with mean-reverting jumps with the value function given by an expansion in Hermite polynomials.
Adrien Treccani - One of the best experts on this subject based on the ideXlab platform.
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pricing american options under high dimensional models with recursive adaptive sparse Expectations
Journal of Financial Econometrics, 2021Co-Authors: Simon Scheidegger, Adrien TreccaniAbstract:We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the Expectation Operator from an exercise period to the previous period. Given that available option databases gather several thousands of prices, there is a clear need for fast approaches in empirical work. Our method processes an entire cross section of options in a single execution and offers an immediate solution to the estimation of hedging coefficients through finite differences. It thereby brings valuable advantages over Monte Carlo simulations, which are usually considered to be the tool of choice in high dimensions, and satisfies the need for fast computation in empirical work with current databases containing thousands of prices. We benchmark our algorithm under the canonical model of Black and Scholes and the stochastic volatility model of Heston, the latter in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process.
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pricing american options under high dimensional models with recursive adaptive sparse Expectations
Social Science Research Network, 2016Co-Authors: Simon Scheidegger, Adrien TreccaniAbstract:We introduce a novel numerical framework for pricing American options in high dimensions. Such settings naturally arise for derivatives with multiple underlying assets, like basket options. They are equally important for single-asset options because high-dimensional models are best capable of capturing observed price dynamics. Yet, higher-dimensional settings come at the cost of a loss of tractability due to the accompanying exponential growth of computational complexity. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the Expectation Operator from an exercise period to the previous one. The algorithm copes with discretely spaced, possibly nonuniform, time grids. This makes it particularly fast for options with a limited number of exercise periods, like Bermudan options, and options for which the optimal exercise schedule is known ex ante. As compared to Monte Carlo simulations, our scheme processes an entire cross section of options in a single execution. It thereby offers an immediate solution to the estimation of hedging coefficients through finite differences and is ideal when multiple related options need to be analyzed. The algorithm is also capable of dealing with discrete dividends with no performance deterioration, thus improving on the documented inefficiency of exercise policies under continuous dividend yield approximations. We benchmark our algorithm under both the canonical model of Black and Scholes and the stochastic volatility model of Heston in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process.
Robert J Elliott - One of the best experts on this subject based on the ideXlab platform.
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discrete time mean field stochastic linear quadratic optimal control problems
Automatica, 2013Co-Authors: Robert J ElliottAbstract:This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear Operators, the problem is formulated as an Operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the Expectation Operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.
Larry Wasserman - One of the best experts on this subject based on the ideXlab platform.
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Rodeo: Sparse Nonparametric Regression in High Dimensions
2018Co-Authors: John Lafferty, Larry WassermanAbstract:We present a method for simultaneously performing bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth in directions where the gradient of the estimator with respect to bandwidth is large. When the unknown function satisfies a sparsity condition, the approach avoids the curse of dimensionality. The method - called rodeo (regularization of derivative Expectation Operator) - conducts a sequence of hypothesis tests, and is easy to implement. A modified version that replaces testing with soft thresholding may be viewed as solving a sequence of lasso problems. When applied in one dimension, the rodeo yields a method for choosing the locally optimal bandwidth.
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rodeo sparse greedy nonparametric regression
Annals of Statistics, 2008Co-Authors: John Lafferty, Larry WassermanAbstract:We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method¯called rodeo (regularization of derivative Expectation Operator)¯conducts a sequence of hypothesis tests to threshold derivatives, and is easy to implement. Under certain assumptions on the regression function and sampling density, it is shown that the rodeo applied to local linear smoothing avoids the curse of dimensionality, achieving near optimal minimax rates of convergence in the number of relevant variables, as if these variables were isolated in advance.
Simon Scheidegger - One of the best experts on this subject based on the ideXlab platform.
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pricing american options under high dimensional models with recursive adaptive sparse Expectations
Journal of Financial Econometrics, 2021Co-Authors: Simon Scheidegger, Adrien TreccaniAbstract:We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the Expectation Operator from an exercise period to the previous period. Given that available option databases gather several thousands of prices, there is a clear need for fast approaches in empirical work. Our method processes an entire cross section of options in a single execution and offers an immediate solution to the estimation of hedging coefficients through finite differences. It thereby brings valuable advantages over Monte Carlo simulations, which are usually considered to be the tool of choice in high dimensions, and satisfies the need for fast computation in empirical work with current databases containing thousands of prices. We benchmark our algorithm under the canonical model of Black and Scholes and the stochastic volatility model of Heston, the latter in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process.
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pricing american options under high dimensional models with recursive adaptive sparse Expectations
Social Science Research Network, 2016Co-Authors: Simon Scheidegger, Adrien TreccaniAbstract:We introduce a novel numerical framework for pricing American options in high dimensions. Such settings naturally arise for derivatives with multiple underlying assets, like basket options. They are equally important for single-asset options because high-dimensional models are best capable of capturing observed price dynamics. Yet, higher-dimensional settings come at the cost of a loss of tractability due to the accompanying exponential growth of computational complexity. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the Expectation Operator from an exercise period to the previous one. The algorithm copes with discretely spaced, possibly nonuniform, time grids. This makes it particularly fast for options with a limited number of exercise periods, like Bermudan options, and options for which the optimal exercise schedule is known ex ante. As compared to Monte Carlo simulations, our scheme processes an entire cross section of options in a single execution. It thereby offers an immediate solution to the estimation of hedging coefficients through finite differences and is ideal when multiple related options need to be analyzed. The algorithm is also capable of dealing with discrete dividends with no performance deterioration, thus improving on the documented inefficiency of exercise policies under continuous dividend yield approximations. We benchmark our algorithm under both the canonical model of Black and Scholes and the stochastic volatility model of Heston in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process.
