Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models

TL;DR

This paper introduces a Sequential Monte Carlo Samplers method leveraging copula dependence to efficiently estimate capital allocations in multivariate risk models, addressing the challenge of conditional expectation calculations under rare events.

Contribution

It presents a novel application of Sequential Monte Carlo Samplers for capital allocation in copula-dependent risk models, improving computational efficiency.

Findings

Efficient estimation of conditional expectations in risk models.

Demonstrated effectiveness through computational examples.

Enhanced accuracy in capital allocation under rare events.

Abstract

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.