Common Shock Models for Claim Arrays

27 Pages Posted: 14 Dec 2016

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: December 14, 2016

Abstract

The paper is concerned with multiple claim arrays. We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles and trapezia that appear in the literature. General forms of dependency are considered, with cell-, row-, column-, diagonal-wise, and other, forms of dependency as special cases.

In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, substantial effort is applied to practical interpretation of such matrices generated by the models constructed here. Indeed, the literature does not document any methodology by which practitioners, who often parametrise those correlations by means of informed guesswork, may do so in a disciplined and parsimonious manner. In fact, this motivated the work presented in this paper.

Reasonably realistic examples are examined, in which an expression is obtained for the general entry in the correlation matrix in terms of a limited set of parameters, each of which has a straightforward intuitive meaning to the practitioner. This will maximise chance of obtaining a reliable matrix. This construction is illustrated by a numerical example. Finally, the generated correlation matrix is then combined with heuristic estimates of tail dependency to arrive at a t-copula which might be used to construct capital margins dealing with the extreme right tail.

Keywords: Cell-wise dependency, Claim array, Claim dependency, Claim triangle, Column-wise dependency, Common shock, Diagonal-wise dependency, Heuristic estimation, Row-wise dependency

JEL Classification: G22, C52, C55

Suggested Citation

Avanzi, Benjamin and Taylor, Greg and Wong, Bernard, Common Shock Models for Claim Arrays (December 14, 2016). UNSW Business School Research Paper No. 2016ACTL07. Available at SSRN: https://ssrn.com/abstract=2881058 or http://dx.doi.org/10.2139/ssrn.2881058

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Greg Taylor (Contact Author)

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Level 6, East Lobby
UNSW Business School Building, UNSW
Sydney, NSW 2052
Australia
+61 421 338 448 (Phone)

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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