Yes We Can (Price Derivatives on Survivor Indices)

26 Pages Posted: 22 Mar 2017

See all articles by M. Martin Boyer

M. Martin Boyer

HEC Montreal - Department of Finance

Lars Stentoft

Department of Economics, University of Western Ontario; Center for Interuniversity Research and Analysis on Organization (CIRANO); Aarhus University - CREATES

Date Written: Spring 2017

Abstract

We propose a simulation approach to value derivatives when the underlying dynamics are estimated using the survivor indices directly. Our results show that survivor forward and swap premiums increase with maturity and with the market price of risk. Our results also confirm that taking the optionality into consideration is important from a pricing perspective, for both U.S. women and men. We compare our results to what is obtained using an alternative modeling approach in which a Lee–Carter model is used to indirectly model the survivor index. Compared to this method, our estimated premiums and prices are higher for all longevity products. Moreover, comparing American‐style with European‐style options we find that, although the early exercise option has value when using survivor indices directly, the relative value of the early exercise option is significantly less than when the Lee–Carter model is used to indirectly model the survivor index. It follows that the assumed mortality dynamics have important implications for the term structure of forward and swap premiums and for the effect that changes in the market price of risk has on them.

Suggested Citation

Boyer, M. Martin and Stentoft, Lars, Yes We Can (Price Derivatives on Survivor Indices) (Spring 2017). Risk Management and Insurance Review, Vol. 20, Issue 1, pp. 37-62, 2017. Available at SSRN: https://ssrn.com/abstract=2938134 or http://dx.doi.org/10.1111/rmir.12073

M. Martin Boyer (Contact Author)

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Lars Stentoft

Department of Economics, University of Western Ontario ( email )

London, Ontario N6A 5B8
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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