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

Yıl 2011, Cilt: 4 Sayı: 2, 69 - 85, 01.06.2011

Ayşe Arık , Meral Sucu

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

• Blake, D., Burrows, W., 2001, Survivor bonds: Helping to hedge mortality risk, Journal of Risk and Insurance 68 (2), pp 339-348.
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• 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.
• Cummins, J.D., 2004, Securitization of life insurance assets and liabilities, Submitted to TIAA-CREF Institute.
• 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.
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• Lane, M.N., 2000, Pricing risk transfer transactions, Astin Bulletin International Actuarial Association, Vol:30, No:2, pp 259-295.
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• Lin, Y., Cox, S.H., 2007, Longevity risk, rare event premia and securitization. Available at SSRN: http://ssrn.com/abstract=1070421.
• McNeil, A., 1997, Estimating the tails of loss severity distributions using extreme value theory, ASTIN Bulletin 27, pp 117_137.
• Pitacco, E., Denuit, M., Haberman, S., Olivieri, A., 2009, Modelling Longevity Dynamics for Pensions and Annuity Business, Oxford University Press.
• Sanders, D.E.A., 2005, The Modeling of Extreme Events, British Actuarial Journal 11 (3), pp 519-572.