A guide to Monte Carlo simulation concepts for assessment of risk-return profiles for regulatory purposes
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A guide to Monte Carlo simulation concepts for assessment of risk‑return profiles for regulatory purposes Stefan Graf1 · Ralf Korn2,3 Received: 30 October 2019 / Revised: 23 April 2020 / Accepted: 30 April 2020 © The Author(s) 2020
Abstract Various regulatory initiatives (such as the pan-European PRIIP-regulation or the German chance-risk classification for state subsidized pension products) have been introduced that require product providers to assess and disclose the risk-return profile of their issued products by means of a key information document. We will in this context outline a concept for a (forward-looking) simulation-based approach and highlight its application and advantages. For reasons of comparison, we further illustrate the performance of approximation methods based on a projection of observed returns into the future such as the Cornish–Fisher expansion or bootstrap methods. Keywords Risk-return profiles of pension products · Customer protection · Regulatory requirements
1 Simulation and its role in regulatory issues The importance of funded private or occupational old age provision will increase due to demographic changes and the resulting challenges for government-run payas-you-go systems. Retail investors and advisors therefore need reliable methodologies to match offered products and investors’ needs and risk appetite. Regulatory issues nowadays typically require the aggregation of the risk of a company, of an investment strategy, a certificate, a pension product or even a short living financial product into a single number. This number might be a fully specified * Ralf Korn [email protected]‑kl.de Stefan Graf s.graf@ifa‑ulm.de 1
Institute for Finance and Actuarial Sciences (IFA), 89081 Ulm, Germany
2
Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany
3
Department of Financial Mathematics, Fraunhofer ITWM, 67663 Kaiserslautern, Germany
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measure such as the variance or the value-at-risk of the final outcome of the investment (just to name two popular such quantities) or a classification into risk classes or chance-risk classes. Examples for this are the calculation of the Solvency Capital Requirement for an insurance undertaking, the assessment of a product’s risk-return profile for packaged retail and insurance-based investment products (so-called ”PRIIPs”), or the chancerisk classification of pension products from a retail investor’s point of view by the so-called PIA (“Produkt Informationsstelle Altersvorsorge”) in Germany. As the terms chance and risk already imply, the outcome of the corresponding financial transaction is not exactly predictable. Thus, a stochastic modelling of this outcome is the appropriate task. The full probabilistic information about the outcome is contained in its probability distribution. However, as the explicit form of this probability distribution is often unknown, various approximation methods have been used/suggested in the past such as • Monte Carlo simulation, i.e. th
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