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ON SURRENDER AND DEFAULT RISKS
Author(s) -
Le Courtois Olivier,
Nakagawa Hidetoshi
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00487.x
Subject(s) - surrender , actuarial science , valuation (finance) , economics , equity (law) , interest rate , context (archaeology) , financial economics , business , finance , paleontology , archaeology , biology , political science , law , history
This paper examines certain types of saving institutions or insurance companies that are subject to surrender and default risks, in a stochastic interest rate context. In the setting under study, investors are endowed with an option to surrender. The goal of the paper is to study how this option impacts the default risk of the issuing company and the value of the contracts it issues. Surrender risk has been extensively studied in arbitrated markets, using trees or least‐squares Monte Carlo methods for valuations, although practitioners often rely on econometric methods. We deal with surrender risk in a third way, assuming policyholders have sets of information and preferences that differ from those of financial market agents, but without relying on econometric methods. In particular, policyholders are supposed to be only partially rational (at least in the financial sense). This is done by modeling surrender risk through a Cox process correlated to the assets and interest rate dynamics. The paper provides formulas for the dynamics of the assets of the issuing firm (these dynamics drive the default time of the company), and for the valuation of liabilities and equity. A numerical illustration is provided.