We consider the problem of efficiently computing the full matrix of second-order sensitivities of a Monte Carlo price when the number of inputs is large. Specifically, we analyze and compare methods with run times of at most O(N T), where N is the dimension of the input and T is the time required to compute the price. Since none of the alternatives from previous literature appears to be satisfactory in all settings, we propose two original methods: the first method is based on differentiation in a distributional sense, while the second method leverages a functional relation between first-and second-order derivatives. The former shows excellent generality and computational times to achieve a given target accuracy. The latter is by far the most effective in at least one relevant example and has theoretical interest in that it is the first practical estimator of the full Hessian whose complexity, as a multiple of that of the only-price implementation, does not grow with the dimension of the problem.

Daluiso, R. (2020). Second-order monte carlo sensitivities in linear or constant time. THE JOURNAL OF COMPUTATIONAL FINANCE, 23(4), 61-91 [10.21314/JCF.2020.381].

Second-order monte carlo sensitivities in linear or constant time

Daluiso R.
2020

Abstract

We consider the problem of efficiently computing the full matrix of second-order sensitivities of a Monte Carlo price when the number of inputs is large. Specifically, we analyze and compare methods with run times of at most O(N T), where N is the dimension of the input and T is the time required to compute the price. Since none of the alternatives from previous literature appears to be satisfactory in all settings, we propose two original methods: the first method is based on differentiation in a distributional sense, while the second method leverages a functional relation between first-and second-order derivatives. The former shows excellent generality and computational times to achieve a given target accuracy. The latter is by far the most effective in at least one relevant example and has theoretical interest in that it is the first practical estimator of the full Hessian whose complexity, as a multiple of that of the only-price implementation, does not grow with the dimension of the problem.
Articolo in rivista - Articolo scientifico
Algorithmic differentiation; Derivatives pricing; Distributional derivative; Functional derivative; Gamma; Greeks;
English
2020
23
4
61
91
partially_open
Daluiso, R. (2020). Second-order monte carlo sensitivities in linear or constant time. THE JOURNAL OF COMPUTATIONAL FINANCE, 23(4), 61-91 [10.21314/JCF.2020.381].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/501219
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