Review of Quantitative Finance and Accounting

, Volume 43, Issue 2, pp 301–331

Tail risk in pension funds: an analysis using ARCH models and bilinear processes

Original Research

DOI: 10.1007/s11156-013-0373-9

Cite this article as:
Owadally, I. Rev Quant Finan Acc (2014) 43: 301. doi:10.1007/s11156-013-0373-9


Pension funding rules and practice contain implicit smoothing and counter-cyclical mechanisms. We set up a stylized model to investigate whether this may give rise to tail risk, in the form of large but rare losses, when pension liabilities are imperfectly but optimally hedged by pension fund assets. We find that pension losses follow a nonlinear dynamic process, and we derive a complete description of the stochastic properties of this process using Markov chain and bilinear stochastic process theory. The resulting pension dynamics resembles that of a modified ARCH model, which suggests that bursts in volatility may occur, and tail risk may be present. Simulations confirm that pension losses exhibit skewness, leptokurtosis and heavy tails, specially when cash flow smoothing is pronounced. Regulators and investors should be aware of the total amount of smoothing in pension funds as this may contribute to extreme losses, which may adversely affect the security of employee benefits as well as the valuation of firms with corporate pension plans.


PensionsRiskHeavy-tailed distributionLARCH process

JEL Classification


Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Cass Business SchoolCity University LondonLondonUK