Uzun ömürlülük bonolarını fiyatlandırma: Uç değer kuramı ve kübik risk fiyatlandırma modeli

Öz

Bu çal mada teknik kazanc ölümlülük endeksine ba l olan bir uzun ömürlülük bonosu fiyatland r lm t r. Ölümlülük endeksinin geli imindeki küçük de i imler sabit terimli (driftli) rasgele yürüyü modeli ile, say ca az olan uzun ömürlülük durumlar ise uç de er teoremine göre modellenmi tir. Uzun ömürlülük bonosu, Lane ve Movchan (1999) taraf ndan geli tirilen kübik risk modeli ile fiyatland r lm t r

Anahtar Kelimeler

• Uzun ömürlülük bonosu, Lee-Carter modeli, Uç de er kuram , Ölüm oran ,Fiyatland rma

Pricing longevity bonds: Extreme value theory and risk cubic pricing model

Öz

The bond which is written on longevity risk has been priced in this study. The payoff is given by

depending on a mortality index. While the small variations in the mortality index are modelled by using

random walk model with drift, rare longevity cases are modelled by extreme value theory. The mortality

modelling is priced by using the risk cubic pricing method which is developed by Lane and Movchan

(1999).

Anahtar Kelimeler

• Longevity bonds,Lee-Carter model,Extreme value theory,Mortality rate,Pricing.

Kaynakça

1. Blake, D., Burrows, W., 2001, Survivor bonds: Helping to hedge mortality risk, Journal of Risk and Insurance 68 (2), pp 339-348.
2. Cairns, A. J. G., Blake, D., Dowd, K., 2005, Pricing frameworks for securitization of mortality risk. Working Paper, Heriot-Watt University, Edinburgh, UK.
3. Chen, H., Cummins, J.D., 2009, Longevity bond premiums:The extreme value approach and risk cubic pricing, Insurance: Mathematics and Economics 46, pp 150-161.
4. Cummins, J.D., 2004, Securitization of life insurance assets and liabilities, Submitted to TIAA-CREF Institute.
5. Denuit, M., Devolder, P., Goderniaux, A., 2007. Securitization of longevity risk: Pricing survivor bonds with wang transform in the Lee_Carter framework, Journal of Risk and Insurance 74 (1), pp 87-113.
6. Gilli, M., Kellezi, E., 2000, Extreme Value Theory for Tail-Related risk measures.
7. Haberman, S., Russolillo, M., 2005, Lee-Carter mortality forecasting:application to the Italian population, Actuarial Research Paper, No:167.
8. Koissi, M-C, Shapiro, A., Högnas, G., 2004, Fitting and forecasting mortality rates for Nordic countries using Lee-Carter method, Department of Mathematics, Abo Academy University, Finland.

9. Lane, M.N., Movchan, O.Y., 1999, Risk cubes or price, risk, and ratings (Part II).Journal of Risk Finance 1 (1), pp 71-86.
10. Lane, M.N., 2000, Pricing risk transfer transactions, Astin Bulletin International Actuarial Association, Vol:30, No:2, pp 259-295.
11. Lee, R.D., Carter, L.R., 1992, Modelling and forecasting U.S. mortality, Journal of the American Statistical Association, No:419, pp 659-675.
12. Lin, Y., Cox, S.H., 2007, Longevity risk, rare event premia and securitization. Available at SSRN: http://ssrn.com/abstract=1070421.
13. McNeil, A., 1997, Estimating the tails of loss severity distributions using extreme value theory, ASTIN Bulletin 27, pp 117_137.
14. Pitacco, E., Denuit, M., Haberman, S., Olivieri, A., 2009, Modelling Longevity Dynamics for Pensions and Annuity Business, Oxford University Press.
15. Sanders, D.E.A., 2005, The Modeling of Extreme Events, British Actuarial Journal 11 (3), pp 519-572.