Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations
| Autor: | Stefano De Marco, Alexandre Zhou, Emmanuel Gobet, Florian Bourgey |
|---|---|
| Přispěvatelé: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC) |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Stochastic control [STAT.AP]Statistics [stat]/Applications [stat.AP] 021103 operations research CVAR Applied Mathematics 0211 other engineering and technologies Estimator 02 engineering and technology Function (mathematics) [QFIN.RM]Quantitative Finance [q-fin]/Risk Management [q-fin.RM] 01 natural sciences Upper and lower bounds [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability Margin (machine learning) Applied mathematics Differentiable function 0101 mathematics Random variable Mathematics |
| Zdroj: | Monte Carlo Methods and Applications Monte Carlo Methods and Applications, De Gruyter, 2020, 26 (2), ⟨10.1515/mcma-2020-2062⟩ |
| ISSN: | 1569-3961 0929-9629 |
| DOI: | 10.1515/mcma-2020-2062 |
| Popis: | The multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations 𝔼 [ g ( 𝔼 [ f ( X , Y ) | X ] ) ] {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]} , where f , g {f,g} are functions and ( X , Y ) {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems. |
| Databáze: | OpenAIRE |
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