key: cord-0972521-u7cph27q authors: Chen, Shi; Yang, Yang; Lin, Jyh-Horng title: Capped borrower credit risk and insurer hedging during the COVID-19 outbreak date: 2020-09-02 journal: Financ Res Lett DOI: 10.1016/j.frl.2020.101744 sha: db5f69f7d64d13de538726ac45c830fa720d3ce5 doc_id: 972521 cord_uid: u7cph27q In this paper, we apply the risk-neutral valuation methodology to evaluate a life insurer's equity. We model the features capped by the explicit treatment of the borrowing firm's credit risk, the optimal guaranteed rate-setting, and the coronavirus disease (COVID-19) outbreak. The results show that the severe effect of the COVID-19 epidemic on the borrowing firm harms its insurance business but that stringent capital regulation helps. The severe impact of COVID-19 on both the borrowing firm and the insurer hedging harm policyholder protection, thereby adversely affecting insurance stability. The year 2020 has seen a fundamental market driver in financial volatility: the global coronavirus disease outbreak (Daniels Trading, 2020) . Due to this pandemic, asset-liability matching management will likely receive renewed focus from insurers and regulators (Scanlan and Delappe, 2020) . Insurance Europe (2014) indicates that insurers usually manage financial volatility by hedging transactions. Moreover, the Board of Governors of the Federal Reserve System (2020) states that the regulators encourage financial institutions to work constructively with borrowing firms affected by the COVID-19 outbreak. These reports form the basis of our modelling in this paper. 4 The purpose of this paper is to develop a capped down-and-out call option model to evaluate the insurer's equity. The features of the model include the capped credit risk from the borrowing firm, the premature risk structure captured by the barrier call, the imperfect competition reflected by the optimal guaranteed rate determination, and the COVID-19 outbreak expressed by the structural break in volatility. We complement the literature of the asset-liability matching management by taking into account the explicit treatment of the borrowing firm's capped credit risk to evaluate the equity of the insurer. We suggest that the capped down-and-out call option model is intimately relevant to the optimal guaranteed rate-setting strategy, policyholder protection, insurer hedging, and the COVID-19 outbreak. In this paper, the down-and-out call option approach (Grosen and Jørgensen, 2002 ) is applied to a life insurer-borrowing firm situation because the recent respectively; however, the policy market is imperfectly competitive, where the insurer is the guaranteed rate-setter (see Polborn, 1998) . The respective balance sheets of the borrowing firm and the insurer at 0 t  are given by: where (1 )   is the insurer leverage and  is capital regulation. Both the balance 5 sheets are linked by a A where the borrowing-firm liabilities equals the insurer's assets. The market value of the borrowing firm's assets varies with the stochastic  the instantaneous standard deviation of the return (i.e., structural break in volatility, Kholodilin and Yao, 2006) The first term on the right-hand side of Eq. (4) is the long down-and-out call on with the strike price . The second term is the short down-and-out call paying the policyholders a fraction  of the positive difference between (1 )   and . These two terms are specified as follows: In Eq. (5), the first term is the standard call pricing value. The second term is the value using the down-and-in call pricing approach, where the barrier ratio / vH  is the barrier value of the insurer assets in which creditors cannot force dissolution. f R is the risk-free rate. Next, the second term in Eq. (4) is given by: where the expression of ((1 ) , ) SC follows a similar argument as in the case of Eq. (5), except that the term in Eq. (5) is replaced by Now, we apply Dermine and Lajeri (2001) to rewrite Eq. (4) as follows: follows a similar argument as in the case of In Eq. (7), , net of a call on b at a strike price . The last two terms are the loss of the value from the cap. Besides, this term needs further deduction of the cost of a down-and-in call on b at 8 a strike price , net of a down-and-in call on b at a strike price . In the second term in Eq. (7), the same pattern as previously applies. The mode determines the optimal guaranteed rate, where /0 Moreover, we model the insurer's liability when considering the capped credit risk from the borrowing firm. The debt is valued as follows: 5) and (6). In Eq. (9), the first term is a long position on a risk-free guaranteed payment, the second term is the price of the equity holders' put to default, and the third term is a long call option on the borrowing firm's underlying assets with the strike price . We further investigate the effects of ( i  b  , a  ,  and )  on policyholder protection. These mathematical results are: where the first term is the direct effect, and the second term is the indirect effect. In the following section, we assess the comparative impacts by assuming some parameter values for the numerical analysis. Before proceeding with the numerical analysis, unless otherwise indicated, the parameter values are assumed as follows: (i) Persson and Aase (1997) find that the loading rates for term insurance contracts are 0.81% for a 20-year-old policyholder, 1.73% for a 30-year-old one, 3.72% for a 40-year-old one, and 6.30% for a 50-year-old one. The average loading rate is 3.14%. ). The upward-sloping feature is due to Polborn (1998) . (ii) The security-market interest rate is approximately 4.00%, as reported by Insurance Europe and Oliver Wyman (2013) . Thus, we assume f R  4.50%. Rudden (2019) reports that the rate of return on life insurers' invested assets in the United States is 7.07% in 2000, 5.70% in 2008, 4.81% in 2015, and 4.72% in 2018. Thus, we assume a R  5.00%. Moreover, the rate of investment returns of the borrowing firm is arbitrary. We assume b R  6.00% for the numerical analysis. (iii) We follow Briys and de Varenne (1994) and assume   0.10 and   0.85. b E is assumed to be 35, which makes the borrower's capital-to-asset ratio fall between 10 9.50% and 12.30%, which is consistent with 11.70% in 2018 of the United States. 3 (iv) Brockman and Turtle (2003) report that the average implied barrier is 0.69, with a corresponding standard deviation of 0.23. Thus, we assume   0.60. Brockman and Turtle (2003) find that asset volatilities display a wide variation from less than 5% to a maximum of over 340% in the corporate security valuation. The mean asset volatility is 0.29. The volatility range is from 0.1 to 0.5 in the study of Briys and de Varenne (1994) . For simplicity, we consider ab   0.20. (v) A part of asset volatility demonstrates the structural break effect in our model. Table 1 demonstrates that the optimal guaranteed rate is negatively related to the severe effect of the COVID-19 outbreak on the borrowing firm. The decreased optimal guaranteed rate (and thus the increased optimal insurer interest margin) results in reducing the life insurance policies, as reduced investment returns are an integral part of the policies themselves in the asset-liability matching management. Our result indicates that the capped down-and-out call option model can be used to explain the COVID-19 impact to a great extent. Table 2 shows that hedging enhances the policies at an increased guaranteed rate when hedging is low, whereas it decreases the policies at a reduced guaranteed rate. The former supports Daniels Trading (2020) . The ambiguous effect suggests that the insurer would have to evaluate its risk management capability and then decide its risk absorption. In Table 3 , we show that capital regulation enhances the life insurance business at an increased guaranteed rate. The insurer makes use of its pricing (guaranteed rate-setting) strategy to attract policyholders. The result implies an important role played by the pricing strategy in the life insurance market. However, the financial authorities usually tend to adapt to prevent a financial crisis by capital regulation.  is various. The direct effect is positive in sign, and the indirect effect is negative. The negative indirect effect is sufficient to offset the positive direct effect. Table 4 shows that an increase in the credit risk of the borrowing firm decreases the policyholder protection, thereby adversely affecting insurance stability. The positive direct effect demonstrates increased policyholder protection. But the negative indirect impact shows the decreased policyholder protection significantly at a reduced optimal guaranteed rate. Mao and Zhang (2020) argue that life insurance is a new business opportunity in the COVID-19 outbreak. Alternatively, we say that the business costs to policyholders are high when the asset-liability matching management focuses on managing capped credit risk and conducting guaranteed rate-setting strategies. (2020), as the hedging is costly. positive. The positive indirect effect is sufficient to offset the negative direct effect when capital regulation is low, and the positive indirect effect is insufficient to offset the negative direct effect when capital regulation is high. and undertake other supportive actions safely. Stringent capital regulation during the COVID-19 outbreak supports our argument. This The reinsurance decision in life insurance firms: an empirical test of the risk-bearing hypothesis Coronavirus disease 2019 (COVID-19). Board of Governors of the Federal Reserve System Life insurance in a contingent claim framework: pricing and regulatory implications A barrier option framework for corporate security valuation Using futures to hedge against coronavirus (COVID-19) risks. Daniels Trading Credit risk and the deposit insurance premium: a note Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework Why insurers differ from banks. Insurance Europe Publication Funding the future: insurers' role as institutional investors. Insurance Europe Global insurance market 16 report Modelling the structural break in volatility New business opportunity emerging in China under COVID-19 outbreak. China Briefing Valuation of the minimum guaranteed return embedded in life insurance products A model of an oligopoly in an insurance market Rate of return on life insurers' invested assets in the COVID-19 update: hedge fund liquidity management considerations