Faiz Oranının Anüite Fiyatları Üzerindeki Etkisine İlişkin Bir Çalışma

Yıl 2024, , 593 - 601, 27.06.2024

Çiğdem Lazoğlu , Müge Yeldan , Uğur Karabey

https://doi.org/10.35414/akufemubid.1406903

Öz

Sigortacılıkta, uzun dönemli anüiteler için doğru iskonto faktörünün belirlenmesi son derece önemlidir. Aktüeryal çalışmalarda iskonto faktörü genellikle sabit olarak ele alınmaktadır; ancak yüksek volatiliteli faiz oranına sahip ülkelerde sabit faiz oranı kullanmak, doğru olmayan hesaplamalara neden olmaktadır. Bu çalışmada farklı ekonomik ve demografik yapılara sahip ülkeler için Monte Carlo Simülasyonu oluşturulmuş, simülasyonda ölümlülük için Lee-Carter modeli, faiz için Vasicek modeli tercih edilerek, sabit ve stokastik faiz ile hayat anüitesi fiyatlarının ampirik olarak dağılımı elde edilmiştir. Risk ölçütleri kullanılarak hem ölümlülükteki hem de faizdeki oynaklığın anüite fiyatları üzerindeki etkisi incelenmiştir. Sonuç olarak faiz oranındaki değişkenlik arttıkça, anüite fiyatlarındaki volatilitenin de yükseldiği belirlenmiştir

Anahtar Kelimeler

Hayat Anüite, Lee-Carter Ölümlülük Modeli, Vasicek Faiz Modeli, Risk Ölçütleri

Importance of Interest Rate on Annuity Prices: A Case Study

Öz

Determination of the accurate discount factor for long-term annuities is crucial in insurance sector. In actuarial studies, the discount factor is typically assumed to be fixed. However using a fixed interest rate in countries with highly fluctuating interest rates can lead to unreliable calculations. In this paper, a Monte Carlo Simulation is constructed for countries with different economic and demographic structures where the Lee-Carter and Vasicek model is used for mortality and interest rate, respectively. Thanks to this scenario the empirical distribution of annuities with both fixed and variable interest rates are established. Risk measures are employed to analyze the impact of mortality volatility and interest rate volatility on the annuity prices. The findings indicate that annuities valued with high interest rate volatility exhibit greater overall volatility. As a result, as the variability of interest rates increases, the volatility of the annuity prices also rises.

Anahtar Kelimeler

Life Annuity, Lee-Carter Mortality Model, Vasicek Short- Rate Model, Risk Measures

Kaynakça

• Beekman, John A., and Clinton P. Fuelling. 1990. “Interest and Mortality Randomness in Some Annuities.” Insurance Mathematics and Economics 9, 185-196. https://doi.org/10.1016/0167-6687(90)90033-A
• Biffis, Enrico, and Michel Denuit. 2011. “Lee-Carter Goes Risk-Neutral.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.848304.
• Boyle, Phelim P. 1976. “Rates of Return as Random Variables.” The Journal of Risk and Insurance 43, 693-713. https://doi.org/10.2307/252033
• Denuit, Michel. 2008. “Comonotonic Approximations to Quantiles of Life Annuity Conditional Expected Present Value.” Insurance: Mathematics and Economics 42, 831-838. https://doi.org/10.1016/j.insmatheco.2007.09.00
• Dowd, Kevin, David Blake, and Andrew J.G. Cairns. 2011. “A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks.” North American Actuarial Journal 15, 237-247. https://doi.org/10.1080/10920277.2011.10597619
• Dufresne, Daniel. 2007. “Stochastic Life Annuities.” North American Actuarial Journal 11, 136-157. https://doi.org/10.1080/10920277.2007.10597441
• Hoedemakers, Tom, Grzegorz Darkiewicz, and Marc Goovaerts. 2005. “Approximations for Life Annuity Contracts in a Stochastic Financial Environment.” Insurance: Mathematics and Economics 37, 239-269. https://doi.org/10.1016/j.insmatheco.2005.02.003
• Lee, Ronald D., and Lawrence R. Carter. 1992. “Modeling and Forecasting U.S. Mortality.” Journal of the American Statistical Association 87, 659-675. https://doi.org/10.1080/01621459.1992.10475265
• Liu, Xiaoming. 2013. “Annuity Uncertainty with Stochastic Mortality and Interest Rates.” North American Actuarial Journal 17, 136-152. https://doi.org/10.1080/10920277.2013.795481
• Pollard, J. H. 1971. “On Fluctuating Interest Rates.” Bulletin De l’Association Royale Des Actuaries Gelges 66, 68–94. https://doi.org/10.2307/1426648
• Rabitti, Giovanni, and Emanuele Borgonovo. 2020. “Is Mortality or Interest Rate the Most Important Risk in Annuity Models? A Comparison of Sensitivity Analysis Methods.” Insurance: Mathematics and Economics 95, 48-58. https://doi.org/10.1016/j.insmatheco.2020.09.001
• Richards, S. J., and I. D. Currie. 2009. “Longevity Risk and Annuity Pricing with the Lee-Carter Model.” British Actuarial Journal 15, 317-365. https://doi.org/10.1017/s1357321700005675
• Vasicek, Oldrich. 1977. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics 5, 177-188. https://doi.org/10.1016/0304-405X(77)90016-2
• Wang, Nan, Russell Gerrard, and Steven Haberman. 2004. “The Premium and the Risk of a Life Policy in the Presence of Interest Rate Fluctuations.” Insurance: Mathematics and Economics 35, 537-551. https://doi.org/10.1016/j.insmatheco.2004.07.004
• https://data.oecd.org/healthstat/life-expectancy-at-65.htm#indicator-chart. (12.02.2024)
• https://biruni.tuik.gov.tr/medas/?locale=tr (11.12.2023)
• https://www.mortality.org (11.12.2023)
• https://finance.yahoo.com/ (10.02.2024)