Market Price of Longevity Risk for a Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing

38 Pages Posted: 12 Feb 2018

See all articles by Michael Sherris

Michael Sherris

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies; UNSW Australia Business School

Yajing Xu

UNSW Australia Business School, School of Risk & Actuarial Studies

Jonathan Ziveyi

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: February 10, 2018

Abstract

The pricing of longevity-linked securities depends not only on the stochastic uncertainty of the underlying risk factors, but also the attitude of investors towards those factors. In this research, we investigate how to estimate the market risk premium of longevity risk using investable retirement indexes, incorporating uncertain real interest rates using an affine dynamic Nelson-Siegel model. A multi-cohort aggregate, or systematic, continuous time affine mortality model is used where each risk factor is assigned a market price of mortality risk. To calibrate the market price of longevity risk, a common practice is to make use of market prices, such as longevity-linked securities and longevity indices. We use the BlackRock CoRI Retirement Indexes, which provides a daily level of estimated cost of lifetime retirement income for 20 cohorts in the U.S. Although investment in the index directly is not possible, individuals can invest in funds that track the index. For these 20 cohorts, we assume risk premiums for the common factors are the same across cohorts, but the risk premium of the factors for a specific cohort is allowed to take different values for different cohorts. The market prices of longevity risk are then calibrated by matching the risk-neutral model prices with BlackRock CoRI index values. Closed-form expressions and prices for European options on longevity zero-coupon bonds are derived using the model and compared to prices for standard options on zero coupon bonds. The impact of uncertain mortality on long term option prices is quantified and discussed.

Keywords: Multi-cohort mortality model, Market price of longevity risk, Longevity indexes

JEL Classification: C13, G22, G23, J11

Suggested Citation

Sherris, Michael and Xu, Yajing and Ziveyi, Jonathan, Market Price of Longevity Risk for a Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing (February 10, 2018). UNSW Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=3121520 or http://dx.doi.org/10.2139/ssrn.3121520

Michael Sherris (Contact Author)

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies ( email )

UNSW Business School
Risk and Actuarial Studies
Sydney, NSW 2052
Australia
+61 2 9385 2333 (Phone)
+61 2 9385 1883 (Fax)

HOME PAGE: http://www.asb.unsw.edu.au/schools/Pages/MichaelSherris.aspx

UNSW Australia Business School ( email )

Sydney, NSW 2052
Australia

Yajing Xu

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

Jonathan Ziveyi

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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