No Access

A QUADRATIC HEDGING APPROACH TO COMPARISON OF CATASTROPHE INDICES

RAGNAR NORBERG

Université de Lyon, Université Lyon 1, Fondation Lyon 1, ISFA, Laboratoire SAF, EA 2429, FR-69366 Lyon, France

Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom

Corresponding author.

Search for more papers by this author

and

OKSANA SAVINA

Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom

Search for more papers by this author

https://doi.org/10.1142/S0219024912500306Cited by:3 (Source: Crossref)

Abstract

The present study addresses the problem of designing a catastrophe derivative that insurers can use to hedge catastrophe-related losses in an incomplete market. The losses are modeled as a doubly stochastic compound Poisson process with shot-noise intensity. The hedging capability of a derivative is measured by the reduction of the mean squared hedging error resulting from optimal trading in the derivative. A general form of this measure is obtained in terms of the coefficients in the martingale dynamics of the loss process and the price process of the derivative. Six specific derivatives, with pay-offs depending in different ways on available catastrophe indices and portfolio data, are compared by the proposed criterion.

Keywords:

References

P. Barrieu and N. El Karoui, Finance and Stochastics 9, 269 (2005). Web of Science, Google Scholar
T. Björk, Y. Kabanov and W. Runggaldier, Mathematical Finance 7, 211 (1997). Web of Science, Google Scholar
C. V. Christensen and H. Schmidli, Insurance: Mathematics & Economics 27, 189 (2000). Web of Science, Google Scholar
D. R. Cox and V. Isham , Point Processes ( Chapman and Hall , London , 1980 ) . Google Scholar
J. D. Cummins, D. Lalonde and R. D. Phillips, Journal of Financial Economics 71, 77 (2004). Web of Science, Google Scholar
H. Föllmer and M. Schweizer, Applied Stochastc Analysis 5, 389 (1990). Google Scholar
S. E. Harrington and G. Niehaus, The Journal of Risk and Insurance 66, 205 (1999). Web of Science, Google Scholar
A. Karr , Point Processes and Their Statistical Inference , 2nd edn. ( Marcel Dekker, Inc. , 1991 ) . Google Scholar
J. A. Major , The Financing of Catastrophe Risk , ed. K. A. Froot ( University of Chicago Press , 1999 ) . Google Scholar
R. Norberg, Finance and Stochastics (2012), DOI: 10.1007/S00780-012-0182-3. Google Scholar
P. Protter , Stochastic Integration and Differential Equations , 2nd edn. ( Springer-Verlag , 2004 ) . Google Scholar
O. Savina, On optimal hedging and redistribution of catastrophe risk in insurance, PhD dissertation, Department of Statistics, London School of Economics and Political Science (2008) . Google Scholar