A contingent claim model of life insurer-bank swap default pricing: strategic substitutes and complements

ABSTRACT

This paper develops a contingent claim framework to examine swap transactions between a life insurer and a bank that bilaterally price default risks. We show that the insurer (the protection buyer in the swap transaction market) regards the optimal bank loan rate as a strategic complement. In contrast, the bank (the protection seller) considers the optimal insurer guaranteed rate as a strategic substitute. Hedging conducted by the insurer enhances profits but hurts policyholder protection. Bank capital regulation harms policyholder protection. Insurer capital regulation leads to bank risk-taking. Capital regulations, as such, would jeopardize insurer-bank performance from a financial stability standpoint.

KEYWORDS:

• Swap transactions
• strategic complement
• strategic substitute
• capital regulation

JEL CLASSIFICATION:

• G21
• G22

Acknowledgments

The authors would like to thank David Peel (editor) and an anonymous referee for their helpful comments and suggestions. The usual disclaimer applies.

Disclosure statement

The authors report no potential conflict of interest.

Notes

¹ The swap transaction between the two parties also involves an intermediary who executes the transaction. For simplicity, the role played by the intermediary is ignored in our model.

² Following Episcopos (2008), we assume that there is a zero rebate on failure in Eq. (4)(4) $-[V(\frac{H}{V}{)}^{2\eta }N(a_3)-Z{e}^{-(R_A-R)}(\frac{H}{V}{)}^{2\eta -2}N(a_4)]$(4) .:

³ Episcopos (2008) uses this formula to value a bank’s liability.:

Additional information

Funding

The National Natural Science Foundation of China under Grant 71603217 (Shi Chen) supports this work.