Hostname: page-component-6766d58669-bp2c4 Total loading time: 0 Render date: 2026-05-18T07:59:40.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Tail risk driven by investment losses and exogenous shocks

Published online by Cambridge University Press:  10 October 2024

Xinyue Man Open the ORCID record for Xinyue Man [Opens in a new window]  and
Qihe Tang Open the ORCID record for Qihe Tang [Opens in a new window]
Xinyue Man*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia
Qihe Tang
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia
*
Corresponding author: Xinyue Man; Email: cynthia.man0515@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a company whose business carries the potential for investment losses and is additionally vulnerable to exogenous shocks. The unpredictability of the shocks makes it challenging for both the company and the regulator to accurately assess their impact, potentially leading to an underestimation of solvency capital when employing traditional approaches. In this paper, we utilize a stylized model to conduct an extreme value analysis of the tail risk of the company under a Fréchet-type and a Gumbel-type shock. Our main results explicitly demonstrate the different roles of investment risk and shock risk in driving large losses. Furthermore, we derive asymptotic estimates for the value at risk and expected shortfall of the total loss. Numerical studies are conducted to examine the accuracy of the obtained estimates.

Keywords

Tail riskshockregular variationmax-domain of attractionuniformity

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 54 , Issue 3 , September 2024 , pp. 712 - 737
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The International Actuarial Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Atanasov, V.A. and Black, B.S. (2016) Shock-based causal inference in corporate finance and accounting research. Critical Finance Review, 5, 207–304.CrossRefGoogle Scholar
Bartik, A.W., Bertrand, M., Cullen, Z., Glaeser, E.L., Luca, M. and Stanton, C. (2020) The impact of COVID-19 on small business outcomes and expectations. Proceedings of the National Academy of Sciences, 117(30), 17656–17666.CrossRefGoogle Scholar
Beirlant, J., Dierckx, G. and Guillou, A. (2005) Estimation of the extreme-value index and generalized quantile plots. Bernoulli, 11(6), 949–970.CrossRefGoogle Scholar
Beirlant, J., Goegebeur, Y., Segers, J. and Teugels, J.L. (2006) Statistics of Extremes: Theory and Applications. England: John Wiley & Sons.Google Scholar
Bernanke, B.S. (1983) Nonmonetary effects of the financial crisis in the propagation of the great depression. American Economic Review, 73(3), 257–276.Google Scholar
Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) Regular Variation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Black, F. and Litterman, R. (1992) Global portfolio optimization. Financial Analysts Journal, 48(5), 28–43.CrossRefGoogle Scholar
Borio, C.E., Farag, M. and Tarashev, N.A. (2020) Post-crisis international financial regulatory reforms: A primer. BIS Working Papers No 859.Google Scholar
Box, G.E. and Tiao, G.C. (1975) Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association, 70(349), 70–79.CrossRefGoogle Scholar
Buitendag, S., Beirlant, J. and de Wet, T. (2019) Ridge regression estimators for the extreme value index. Extremes, 22, 271–292.CrossRefGoogle Scholar
Cantelmo, A., Melina, G. and Papageorgiou, C. (2023) Macroeconomic outcomes in disaster-prone countries. Journal of Development Economics, 161, 103037.CrossRefGoogle Scholar
Cochrane, J.H. (1991) A simple test of consumption insurance. Journal of Political Economy, 99(5), 957–976.CrossRefGoogle Scholar
Cox, S.H., Fairchild, J.R. and Pedersen, H.W. (2000) Economic aspects of securitization of risk. ASTIN Bulletin, 30(1), 157–193.CrossRefGoogle Scholar
de Haan, L. and Ferreira, A. (2006) Extreme Value Theory: An Introduction. New York: Springer.CrossRefGoogle Scholar
Dekkers, A.L., Einmahl, J.H. and de Haan, L. (1989) A moment estimator for the index of an extreme-value distribution. The Annals of Statistics, 17(4), 1833–1855.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events: For Insurance and Finance. Heidelberg: Springer Berlin.CrossRefGoogle Scholar
Fedotenkov, I. (2020) A review of more than one hundred Pareto-tail index estimators. Statistica, 80(3), 245–299.Google Scholar
Fraga Alves, M.I., Gomes, M.I., de Haan, L. and Neves, C. (2009) Mixed moment estimator and location invariant alternatives. Extremes, 12, 149–185.CrossRefGoogle Scholar
Frees, E.W., Carriere, J. and Valdez, E. (1996) Annuity valuation with dependent mortality. Journal of Risk and Insurance, 63(2), 229–261.CrossRefGoogle Scholar
Froot, K.A. (2001) The market for catastrophe risk: A clinical examination. Journal of Financial Economics, 60(2-3), 529–571.CrossRefGoogle Scholar
Gomes, M.I. and Guillou, A. (2015) Extreme value theory and statistics of univariate extremes: A review. International Statistical Review, 83(2), 263–292.CrossRefGoogle Scholar
Hashorva, E., Pakes, A.G. and Tang, Q. (2010) Asymptotics of random contractions. Insurance: Mathematics and Economics, 47(3), 405–414.Google Scholar
Lindskog, F. and McNeil, A.J. (2003) Common Poisson shock models: Applications to insurance and credit risk modelling. ASTIN Bulletin, 33(2), 209–238.CrossRefGoogle Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2015) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton: Princeton University Press.Google Scholar
Merton, R.C. (1976) Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125–144.CrossRefGoogle Scholar
Miklian, J. and Hoelscher, K. (2022) SMEs and exogenous shocks: A conceptual literature review and forward research agenda. International Small Business Journal, 40(2), 178–204.CrossRefGoogle Scholar
Molk, P. and Partnoy, F. (2019) Institutional investors as short sellers. Boston University Law Review, 99(3), 837–872.Google Scholar
Ng, K.W., Tang, Q. and Yang, H. (2002) Maxima of sums of heavy-tailed random variables. ASTIN Bulletin, 32(1), 43–55.CrossRefGoogle Scholar
Pankratz, N., Bauer, R. and Derwall, J. (2023) Climate change, firm performance, and investor surprises. Management Science, 69(12), 7352–7398.CrossRefGoogle Scholar
Ramelli, S. and Wagner, A.F. (2020) Feverish stock price reactions to COVID-19. The Review of Corporate Finance Studies, 9(3), 622–655.CrossRefGoogle Scholar
Resnick, S.I. (1987) Extreme Values, Regular Variation and Point Processes. New York: Springer.CrossRefGoogle Scholar
Resnick, S.I. (2007) Heavy-tail Phenomena: Probabilistic and Statistical Modeling. New York: Springer.Google Scholar
Röglinger, M., Plattfaut, R., Borghoff, V., Kerpedzhiev, G., Becker, J., Beverungen, D., vom Brocke, J., Van Looy, A., del-Ro-Ortega, A., Rinderle-Ma, S. and Rosemann, M. (2022) Exogenous shocks and business process management: A scholars’ perspective on challenges and opportunities. Business & Information Systems Engineering, 64(5), 669–687.CrossRefGoogle Scholar
Tang, Q. (2008) From light tails to heavy tails through multiplier. Extremes, 11(4), 379–391.CrossRefGoogle Scholar
Tang, Q. and Tsitsiashvili, G. (2004) Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments. Advances in Applied Probability, 36(4), 1278–1299.CrossRefGoogle Scholar
Tang, Q. and Yang, F. (2012) On the Haezendonck–Goovaerts risk measure for extreme risks. Insurance: Mathematics and Economics, 50(1), 217–227.Google Scholar
Tang, Q. and Yuan, Z. (2014) Randomly weighted sums of subexponential random variables with application to capital allocation. Extremes, 17, 467–493.CrossRefGoogle Scholar