Do bond market participants care about directors’ and officers’ liability insurance?——Empirical evidence based on the pricing of corporate bonds

ABSTRACT Based on the risk hedging perspective, this paper examines the impact of directors’ and officers’ liability insurance (hereafter referred to as D&O liability insurance) on the pricing of corporate bonds. We find that the purchase of D&O liability insurance can effectively reduce corporate bond insurance pricing. The path test shows that the purchase of D&O liability insurance can reduce the bond insurance pricing by improving the quality of company’s internal control. Furthermore, the paper finds that when management power is greater, investor protection is poor or financial risk is high,the impact of the D&O liability insurance is stronger. After purchasing D&O liability insurance, creditors will reduce the use of corporate governance contractual terms, but will set more investments and financing as well as option contractual terms. In addition, companies that purchase D&O liability insurance issue bonds with higher credit ratings and longer bond maturities.


Introduction
The bond market is an important part of the capital market, and its healthy development is conducive to improving the efficiency of allocation of market resource and promoting the smooth operation of the capital market. In 2021, China's bond market issue a total of RMB 61.9 trillion of various bonds, an increase of 8% over the previous year. This had a significant impact on the supply-side reform of financing and stimulating the vitality of market players. However, the development of China's bond market late started, and the long-standing belief in rigid payment has seriously distorted the risk pricing mechanism and damaged the efficiency of market resource allocation. The default of the Chaori Bond on interest officially broke the belief in rigid repayment and opened the prelude to the wave of defaults on China's credit bonds. The default of the AAA-rated state-owned enterprise bond Yongmei Bond in 2020 intensified market panic and weakened the investment enthusiasm of investors in the bond market. In this context, discussing the bond investor protection mechanism has far-reaching significance for reducing the risk of a bond default, protecting the rights and interests of creditors, and promoting the reasonable pricing of bonds. Among the many investor protection mechanisms, insurance can undoubtedly play the best role in risk hedging, transferring economic compensation risks to third-party insurance companies to protect the interests of investors.
Directors' and officers' liability insurance (hereafter referred to as D&O liability insurance) is an insurance policy that provides coverage for the risky decisions made by insured directors and management in the course of their employment, with the insurer being responsible for reimbursing the directors or managers for their civil liability. Europe's largest insurance group, Allianz, clearly mentioned in the 2016 Directors and Executives Liability Insurance Insights: Managers' Responsibility Today report: In Asia, the main cause of executive liability insurance claims is related to securities and bond issuance. Nearly half of the 28 Sci-Tech Innovation Board companies in the early days of the China Sci-Tech Innovation Board purchased D&O liability insurance to protect the interests of executives and investors. The advantage of D&O liability insurance is the introduction of a third-party insurer to provide risk compensation and wealth protection for managers' decision errors, thereby increasing their risk tolerance (Core, 2000). Previous studies have found that purchasing D&O liability insurance can enhance corporate value , improve risk-taking , reduce agency costs (Ling & Bai, 2017), and curb stock price crash risk (Yuan et al., 2016). However, while D&O liability insurance plays a role in risk hedging, it induces opportunistic behaviour of management, which reduces the performance of company mergers and acquisitions , increases loan spreads (Lin, Officer, et al., 2013) and aggravates earnings management behaviour (Hu & Zhao, 2017), and increases the cost of equity financing (Feng et al., 2017). The completely different corporate governance effects produced by the subscription of D&O liability insurance lay the foundation for this study. Bonds are an important part of corporate financing. How will the company's purchase of D&O liability insurance affect future bond issuance?
The pricing of bond issuance is determined by the possibility that the issuer cannot repay the debt and the degree of protection of the lender in the event of default (Weinstein, 1981). Lowering the pricing of bond issuance can help companies reduce financing costs and promote corporate health development. Bond characteristics such as repurchase terms, repayment sequence, size, and liquidity (Frank & Driessen, 2012;Harris & Piwowar, 2006;Merton, 1974) are important factors that affect bond financing costs. In recent years, some scholars have found that stablishing a central bank collateral framework (Huang & Guo, 2021) and multiple credit ratings (Chen et al., 2021) are conducive to reducing bond financing costs. The establishment of environmental protection courts (Gao & Wen, 2021) and the equity pledge of controlling shareholders  have increased the cost of bond financing. The insurance system can protect the risk behaviour of executives and protect the rights and interests of creditors. However, few scholars pay attention to the impact of the insurance system of companies on the bond market. Theoretically, the company's subscription to D&O liability insurance has two distinct effects on bond issuance. On the one hand, subscribing to D&O liability insurance can play a supervisory effect, improving corporate governance and information quality. In the event of a company's failure to pay, D&O liability insurance can provide adequate indemnity to the suing party, reducing losses in the event of a bond default, and thus reducing the risk premium at the time of the bond issue. On the other hand, subscription to D&O liability insurance protects management's risky behaviour and then increases risk tolerance. Management will implement more aggressive strategic decisions, while bond investors are averse to aggressive risk strategies. D&O liability insurance can easily induce moral hazard of management , and creditors will then demand a higher risk premium as compensation. Therefore, how the subscription of D&O liability insurance will affect the pricing of corporate bond issuance is an empirical question with research tension.
This paper selects 2007-2020 corporate bonds as the research object and explores the role of the subscription of D&O liability insurance in the bond market. (1) We find that the company's subscription to D&O liability insurance reduces the cost of bond financing. Our results remain stable after a series of robustness tests, indicating that D&O liability insurance plays an active governance role in China's bond market.
(2) Further analysis of its influence mechanism, we find that the subscription of D&O liability insurance can reduce the pricing of corporate bonds by improving the quality of the company's internal control. (3) The impact of the D&O liability insurance on the pricing of corporate bonds is stronger when management has more power, poorer investor protection or higher financial risk. (4) After purchasing D&O liability insurance, creditors reduce the use of corporate governance contractual terms, but will set more investment & financing contractual terms as well as option contractual terms to limit strategic behaviour of corporate risk to protect their rights and interests. (5) In addition, the bonds issued by companies that subscribe to D&O liability insurance have higher credit ratings and longer bond maturities.
Our paper contributes to the literation in several ways. First, it is the first paper to discuss the influencing factors of pricing of corporate bonds from the perspective of risk hedging. Existing literature mainly focuses on the implicit guarantee of local governments (Ao et al., 2017;Bhojraj & Sengupta, 2003;Bonsall et al., 2017;Han & Hu, 2015), and the impact of third-party insurers on the bond issue pricing has not received much attention. Based on the insurance system of D&O liability insurance, this paper discusses its impact on the pricing of bond issuance and enriches the relevant research on the pricing of corporate bonds.
Second, it deepens and expands the research on the governance effect of D&O liability insurance. Existing studies mainly focus on the impact of D&O liability insurance on enterprise value (K. F. Li & Liao, 2014;, corporate governance (Hu & Zhao, 2017;Ling & Bai, 2017), cost of capital (Feng et al., 2017;, risktaking , and stock price crash risk (Yuan et al., 2016). Following previous research, this paper analyzes the relationship & mechanism between D&O liability insurance and bond issuance & pricing, and further supplements the research on the governance effect of D&O liability insurance.
Thirdly, we analyse the mechanism and effect of D&O insurance in reducing the pricing of bond issuance. This paper finds that D&O insurance reduces bond issuance pricing by improving the quality of corporate internal control. There is a stronger governance effect in firms with greater management power, lower levels of investor protection, and greater risk of bankruptcy. Providing empirical clues as to how D&O liability insurance plays the role in corporate governance. GAC Changfeng (600,991) created a precedent for China's D&O liability insurance compensation. In mid-November 2011, GAC Changfeng Moto Co., Ltd. reached an agreement with 15 plaintiffs including the defendant, Li Mou, to pay a total of RMB 980,000 for the loss of investment difference, stamp duty loss, interest loss, and litigation costs. AIG China paid RMB 800,000 to GAC Changfeng Company, and it was the first step in the settlement of claims in China's D&O liability insurance cases. On 22 July 2019, the Sci-Tech Innovation Board Market opened, and listed companies in the biomedical, high-tech, and new energy industries have significantly increased their demand for insurance, which has promoted the rapid development of D&O liability insurance. In March 2020, the implementation of the new Securities Law increased the penalties for securities violations by directors, supervisors, and senior managers of listed companies, greatly increased the number of claims and compensation amounts that listed companies may face, and increased the risk exposure of directors and executives. The Luckin Coffee Accounting Fraud in April 2020 further brought the D&O liability insurance into the public eye. The D&O liability insurance purchased by Luckin Coffee Inc was as high as 25 million US dollars. At present, the company has applied for a claim to the insurance company, but there is still some uncertainty about the settlement of claims. On 12 November 2021, in the first-instance judgement of Kangmei Pharmaceutical's False Statement Civil Litigation Case, a total of 52,037 investors finally received RMB 2.459 billion in compensation, and this pushed D&O liability insurance into the public view. As of the end of October 2021, 650 D&O liability insurance companies are insured, with an insurance coverage rate of about 15%.
Then, is D&O liability insurance leading to more bond claims because of its negative governance effect, or is it having a better bottom-up effect and taking responsibility proactively to reduce default losses? However, exactly what role it plays is unclear and requires further empirical testing.

Theoretical analysis and research assumptions
The existing literature believes that the pricing of corporate bonds is closely related to default risk. The lower the risk of default, the stronger the ability of the company to repay the principal and interest on maturity, and the lower the risk premium demanded by creditors as risk compensation (Altman & Rijken, 2004;Elton et al., 2001). Default risk is mainly related to the level of corporate governance and the ability to cope with risks. The lower the company's financial leverage (Goh & Ederington, 1993), the larger the scale (Chen & Guo, 2008) and the stronger the bond liquidity (Campbell & Taksler, 2003), the less risk a company faces during its operation, and the more likely it is to repay the principal and interest on time, thereby reducing the cost of bond financing. The higher the quality of the company's internal control (Ao et al., 2017), the higher the shareholding ratio of institutional investors (Bhojraj & Sengupta, 2003), and the lower the degree of information asymmetry (Bonsall et al., 2017;H. Zhou et al., 2012), the weaker the management's motivation and ability to grab personal benefits, and the lower the probability of the company's failure to operate, which reduces the probability of future bond defaults from the root cause. The implicit guarantee of the local government plays an important role in the pricing of bond issuance (Han & Hu, 2015;L. Wang & Chen, 2015). Implicit guarantee institutions such as the government can cover the company's default and protect the interests of investors. Therefore, when bonds have implicit guarantees, their issuance are priced relatively low. To sum up, it can be seen that the quality of information, the level of corporate governance and the implicit guarantee are important factors that reduce the pricing of bond issuance. This paper attempts to examine the impact of the subscription of D&O liability insurance on the pricing of bond issuance from two levels of external supervision hypothesis and opportunistic hypothesis.

External oversight hypothesis
D&O liability insurance underwriting companies can exert the effect of external supervision, restrain the self-interested behaviour of the management, improve the level of corporate governance, reduce the risk of future default, and then reduce the pricing of bond issuance. The hypothesis of external supervision effect holds that in order to reduce risks and make full compensation, insurance companies will conduct effective risk assessments on the insured enterprises before taking the insurance, and decide whether to accept the business and design corresponding insurance clauses according to the assessment results. To supervise business decision-making and other aspects to ensure the compliance of enterprises, and play the role of external supervision (O'Sullivan, 2002). When evaluating the risk exposure of insured companies, insurance companies will pay full attention to the past behaviour of directors and executives that may lead to future litigation risks, and tailor insurance policies for each company, thereby improving the effectiveness of supervision. A series of literature show that D&O liability insurance plays an active role in external supervision, which can effectively reduce the company's future stock price crash risk (Yuan et al., 2016), financial restatement (Yuan et al., 2018), and corporate non-compliance probability (C. Li & Xu, 2020), and improve the company's internal control system (Liu et al., 2021). Since the macroeconomic environment and the micro-enterprise environment to which the company belongs have their own risk characteristics in the process of governance, insurance companies can't provide insurance agreements to insured companies in a standardised format during the underwriting process. Examination of historical evidence of company operations is often the basis for insurance companies to assess their risk of claims, on which insurance companies can formulate relevant premium and insurance policy policies for different company risk characteristics . This paper expects underwriting companies to charge higher premiums, lower liability premiums, and stricter insurance terms to listed companies with higher default risks to reduce default risk losses. In addition, By actively participating in corporate governance, insurance companies can discipline companies for false disclosures or other violations, which in turn improves the quality of corporate governance and reduces default risk, allowing bond market participants to claim lower risk premium compensation. Based on this, we propose the following hypothesis: H1a: Based on the external supervision hypothesis, subscribing to D&O liability insurance can reduce the pricing of bond issuance.

The opportunistic hypothesis
The risk underwriting role played by D&O liability insurance reduces the deterrent effect of the law, induces opportunistic management behaviour and raises the risk of corporate default, which increases the pricing of bond issues. Subscribing for D&O liability insurance can provide the bottom line for the management's risky behaviour, improve the risk tolerance of the company's management (Parsons, 2003), and motivate the management to implement corporate innovation, differentiation strategies, and other risk strategic decisions (Hu & Wang, 2019;. However, risk strategy decisions such as corporate innovation require a lot of financial support on the one hand, and financing methods such as equity pledges, short-term loans, and long-term investment aggravate the potential risks of creditors (Lai et al., 2019;Shi et al., 2021). With high uncertainty, once these major decisions fail, the company will face financial difficulties and the bonds will not be able to repay the principal and interest. Creditors are risk-averse investors, and the high-risk business strategy is contrary to the original intention of creditors to invest, and thus demand higher risk premium compensation. In addition, the risk-taking effect of D&O liability insurance is likely to induce opportunistic behaviours in management, and management is more likely to conduct mergers and acquisitions based on its private benefits (Hao & Hu, 2014), which reduces the performance of corporate mergers and acquisitions , aggravates the the degree of earnings management (Hu & Zhao, 2017), the occurrence of these behaviours to a certain extent means the failure of the internal control system. The conflict between management and investor agents would intensify after purchasing D&O liability insurance, and the company faces higher operational risks. Therefore, D&O liability insurance increases the likelihood that the company gets into financial distress, i.e. unable to pay its principal and interest, resulting in a higher risk of default and higher issuance rates demanded by creditors. Overall, this paper proposes the following hypothesis: H1b: Based on the opportunistic hypothesis, the subscription of D&O liability insurance will increase the pricing of bond issuance.

Sample selection and data sources
This paper takes the corporate bonds issued by A-share listed companies in Shanghai and Shenzhen from 2007 to 2020 as the initial sample. We use 2007 as the starting point of our sample period since the issuance of the first corporate bonds approved by China in 2007. Following existing research (Shi et al., 2017;B. Wang & Shi, 2014), we filter the data: (1) This paper excludes ST and *ST companies due to their particularity; (2) Accounting of listed companies in the financial industry Compared with other industries, the treatment is quite different, and this article will exclude them; (3) We exclude delisted companies. After screening, we finally obtain 1522 observations. We winsorise all continuous variables at the 1st and 99th percentiles of their respective distributions to eliminate the influence of extreme values. Details of corporate bonds are from the Corporate Bond Prospectus or Corporate Bond Issuance Announcement. The data of D&O liability insurance is obtained manually from the disclosure of shareholders' meetings, board of directors, and annual reports of each listed company. The rest of the data are from the WIND and CSMAR databases.

Pricing of corporate bonds
This paper uses the bond credit spread (Creditspread) to measure the pricing of bond issuance, that is, the interest rate at the time of bond issuance minus the yield to maturity of treasury bonds with the same maturity structure (Pan et al., 2019). As the bond with the highest credit in the bond market, treasury bonds are the benchmark for the pricing of various other bonds and are closely related to the operation of the macroeconomy (Diebold & Li, 2006;Niu et al., 2016). In this paper, the bond credit spread is the issuance rate of corporate bonds minus the yield to maturity of treasury bonds with the same maturity structure, thereby reducing the impact of the macroeconomic environment on bond pricing.

Directors and executives liability insurance
This paper draws on the practice of  and , and sets a dummy variable (Ins) to measure whether to purchase D&O liability insurance. Specifically, our variable of interest Ins, describing whether the company purchases D&O liability insurance, is a dummy variable. The variable is equal to 1 when the Board of Directors proposes the purchase of D&O liability insurance and the proposal is voted through in the shareholders' proxy meeting, or when there is information about the purchase of this insurance in the announcement of the shareholders' proxy meeting, otherwise it is 0.

Other variables
Drawing on the methods of H. Zhou et al. (2012), Shi et al. (2017), and Lin et al. (2019), this paper controls the characteristics of corporate bonds: bond size (Bondsize), bond maturity (Maturity), bond rate type (Ratetype), bond guarantee (Guarantee); referring to , it controls company characteristics: company size (Size), asset-liability ratio (Lev), return on total assets (ROA), loss (Loss), listing date (Age) and the nature of property rights (SOE). In addition, we also control the fixed influence of industry and year, see, Table 1 for variable definitions for details.

Models
In this paper, the OLS model is used to verify the H1. The specific model is as follows: If H1a holds, the coefficient of Ins should be significantly negative, while the coefficient of Ins should be significantly positive if H1b holds.

Ins
The variable is equal to 1 if the firm purchase the D&O liability insurance, and otherwise is 0. Control variables

BOND CHARACTERISTICS Bondsize
Bondsize is defined as the logarithm of the size of the bonds issued.

Maturity
Maturity is Bond issuance period.

Ratetype
Ratetype is type of bond issue rate that equals 1 if the rate is floating and progressive and 0 if the rate is fixed.

Guarantee
Guarantee is whether the issue of bonds is secured that equals 1 if there is a thirdparty guarantee, and 0 otherwise.

COMPANY CHARACTERISTICS Size
Size is defined as the natural logarithm of total book assets at the end of the period.

ROA
ROA is return on total assets, defined as Net profit/Total assets.

Lev
Lev is assets and liabilities, defined as total responsibility/total assets.

Loss
Loss is whether there was a loss in the previous year that equals 1 if there was a loss, and 0 otherwise.

Age
Age is defined as the natural logarithm of the difference between the bond issue date and listing date.

SOE
The variable equals 1 if it is a state-owned enterprise, and 0 otherwise.

Indu
Indu is an industry dummy variable. The SEC industry code for manufacturing is retained to the last digit of the letter, while others are retained only the first digit.

Year
Year is a dummy variable. The sample interval is 2007-2020.
remaining control variables are more consistent with existing research and will not be elaborated upon. Table 3 presents the regression results for D&O liability insurance and bond issue pricing. Column (1) presents the results of the regression between Ins and Creditspread with a coefficient of −0.530 and significant at the 1% statistical level, indicating that the purchase of D&O liability insurance is negatively related to the spread of bond issues. Column (2) further controls bond issurance characteristics and the findings are largely unchanged. Column (3) controls firm characteristics on the basis of column (2), with a coefficient of −0.174 and significant at the 1% statistical level for Ins. The above findings support H1a, indicating that the purchase of D&O liability insurance can play a role in external supervision, improve corporate governance, reduce the risk of corporate default and thus reduce the pricing of bond issues. As for the control variables, Bondsize and Maturity are negatively related to Creditspread, which may be explained by the fact that companies with low default risk are able to issue larger and longer maturity bonds, and the credit spreads of bonds issued by such companies are also relatively low; firm size (Size), return on total assets (ROA) and nature of ownership (SOE) are negatively related to Creditspread, indicating that the larger the company and the better its business performance, the stronger its ability to resist risk and the lower the risk of bond default. When the bond issuer is a state-owned enterprise, there is an implicit government guarantee and the bond default loss is lower, thus the lower the bond issue pricing. Corporate financial leverage (Lev) is positively correlated with bond issue pricing, indicating that the higher the financial leverage of a company, the higher the operational risk and the higher the risk premium compensation demanded by bond investors.

Influencing channel inspection: internal control quality
In the previous section, we explored the impact of subscription to D&O liability insurance on bond issue pricing from the external monitoring hypothesis and the opportunistic hypothesis, and empirically tested that subscription to D&O liability insurance helps to reduce bond issue pricing. In this section, we further explore the channels underlying the impact of D&O liability insurance on bond issue pricing. Internal control refers to the methods of self-adjustment, discipline, planning, evaluation and control that a company adopts within the enterprise to achieve its business objectives and to ensure the truthfulness and reliability of accounting information. The positive effect of internal control quality on bond issuance has been unanimously recognised by scholars, for example, high-quality internal control can effectively improve bond credit ratings and reduce bond financing costs (Ao et al., 2017;, while subscription to D&O liability insurance can improve the quality of a company's internal control, inhibit management's opportunistic behaviour and reduce the probability of financial restatement (Yuan et al., 2018). We expects that subscribing to D&O liability insurance can improve the quality of a company's internal control and thus influence the pricing of bond issues, that insurers can set stricter insurance terms for companies with higher default risk to reduce default risk losses, and that insurers can actively participate in corporate governance to restrain companies from false disclosures or other illegal behaviours, improve the quality of internal control and reduce default risk. This section therefore further tests whether the quality of internal controls is a possible pathway for subscription to D&O liability insurance to influence the pricing of bond issues. The numbers in parentheses are T values. ***, ** and * represent significance at the level of 1%, 5%, and 10% respectively. All standard errors have been adjusted for robustness.
Referring to the mediation effect test methods of Wen et al. (2004) and Yuan et al. (2018), this paper uses models (1)-(3) to test whether the subscription of D&O liability insurance affects bond issuance and pricing through the quality of internal control.  Baron & Kenny (1986), The Sobel Z test was −2.386 and was significant at the 5% statistical level, indicating that the quality of internal control played a partial mediating effect. The above results show that the subscription of D&O liability insurance can improve the quality of the company's internal control, inhibit the opportunistic behaviour of management, reduce the risk of bond default and affect the pricing of bond issuance.

D&O liability insurance and pricing of corporate bonds: the impact of management power
The previous analysis demonstrates that D&O liability insurance underwriters are able to exert an external oversight effect that restrains management's self-interest, improves corporate governance, reduces the risk of future defaults, and in turn reduces the pricing of bond issues. When management has more power, executives are more likely to extract private benefits through on-the-job spending (T. Zhang & Sha, 2014), exacerbating corruption (M. Zhou et al., 2016) and making corporate agency problems more serious. At this time, D&O liability insurance can play a stronger role of external supervision and governance, restrain management's opportunistic behaviour, inhibit management's onthe-job consumption and other private profit-grabbing behaviours, improve corporate governance and reduce bond default risk. Therefore, we expects that when the management has more power, the subscription to D&O liability insurance can play a stronger role in external monitoring and governance, and the negative relationship with bond issue pricing is more significant.

D&O liability insurance and pricing of corporate bonds: implications for investor protection
The external oversight hypothesis focuses on the principal-agent theory, in which a company uses funds for risky investments to the detriment of creditors in a situation of information asymmetry, and when the company subscribes to D&O liability insurance, the company passes the risk to a third-party insurer, which is required to pay for litigation claims against the insured manager for actions detrimental to shareholders' interests. As indirect bearers of the consequences of a manager's actions, insurers have a greater incentive than other supervisors to exercise their supervisory powers. This paper expects that when bond market participants face weak investor protection mechanisms, the purchase of D&O liability insurance by companies can be more effective in providing external oversight, discouraging management from taking personal advantage and reducing the pricing of bond issues. Therefore, the paper expects that the negative relationship between the subscription to D&O liability insurance and bond issue pricing is more significant when the investor protection mechanism is weak. Notes: The numbers in brackets are T values. ***, **, and * represent significance at 1%, 5%, and 10% levels, respectively. All standard errors have been adjusted for robustness. All control variables are the same as the model (1). To be consistent, to save space, we do not report control variables and intercept terms.

D&O liability insurance and pricing of corporate bonds: the impact of financial risk
The pricing of bond issues is mainly concerned with the company's ability to repay capital and interest on maturity, and subscription to D&O liability insurance can, on the one hand, play an external supervisory role, improve corporate governance and reduce the company's financial risk; on the other hand, D&O liability insurance can play the role of a third party default underwriter. Creditors are compensated and losses from bond defaults are reduced. We expects that when a company's financial risk is high, D&O liability insurance will play a stronger role in external oversight and governance, reducing the company's financial risk, and when a company has difficulty raising funds quickly to pay capital and interest in the event of a default, D&O liability insurance will play a third-party guarantee role, reducing bond default losses. Therefore, we expects that the negative relationship between subscription to D&O liability insurance and bond issue pricing is more significant when the financial risk is high.

A cross-sectional analysis
In order to test the above hypothesis, this paper draws on the research method of , and uses whether the two positions of the management are combined to measure the power. If the chairman and the general manager are the same person, it is considered that the management has more power, otherwise less power. Referring to the method of H. Zhang and Wang (2018), the investor protection index of Beijing Technology and Business University was used to measure the degree of investor protection from the dimensions of accounting information quality, internal control, external audit and financial operation. If above the median, the investor protection level is considered to be high, otherwise, the investor protection level is considered to be low; the financial risk adopts the bankruptcy risk Z index in the WIND database. The larger the index, the lower the bankruptcy risk. If the Z index is higher than the annual median, the financial risk is considered low, otherwise the financial risk is high. This paper re-estimates the model (1) according to management power, investor protection and financial risk grouping, and the test results are shown in Table 5. Columns (1) and (2) show that when the management has great power., the regression coefficient of Ins is −0.888 and is significant at the 1% level. When the management has little power., the regression coefficient of Ins is −0.141 and is significant at the 5% level; we carried out the coefficient difference test between groups, the coefficient difference is −0.747 and significant at the 1% level, above results show that when the management has great power, the external supervision effect of D&O liability insurance is stronger. It has a more significant effect on reducing the default risk of bonds, and thus has a stronger impact on the pricing of bond issuance. Columns (3) -(6) also support our hypothesis.

The influence of D&O liability insurance on bond contractual terms
Bond contractual terms are an important part of corporate bonds, which can effectively reduce the risk of bond default and protect the rights and interests of bond investors. Default risk is a key influence on the setting of bond contractual terms (Billett et al., 2006), and the higher the level of corporate governance, the lower the bond contractual terms (Qi et al., 2011). T. Wang and Shi (2021) find, based on Chinese corporate bonds, that institutional investors mitigate agency conflicts between bond issuers and bond investors by improving corporate governance and the information environment, thereby reducing the use of restrictive bond contractual terms. We expects the purchase of D&O liability insurance to have two distinct impacts on the setting of bond contractual terms. On the one hand, D&O liability insurance plays an external monitoring and governance role, improving corporate governance and reducing the use of corporate governance contractual terms; on the other hand, D&O liability insurance creates a risk-pocketing effect on management's financial risk, inducing management to act opportunistically and implement risky decisions such as innovation and differentiation strategies. If these major decisions fail, the company will be in financial difficulty and will not be able to repay its capital and interest. Therefore, creditors may set more restrictive terms on investment and financing for companies subscribing to the D&O liability insurance, such as suspending major foreign investments and restricting the pledge of assets to protect their rights and interests.
Drawing on the research of Shi et al. (2017), in this paper, the contractual terms of corporate bonds are divided into investment & financing contractual terms (moratorium on major foreign investments, restrictions on acquisitions or mergers, restrictions on the sale of assets, restrictions on pledging assets and restrictions on connected transactions), corporate governance corporate contractual terms (restrictions on dividends to shareholders, restrictions on executive remuneration and non-transferability of key responsible persons) and option contractual terms (adjustable interest rates, early repayment, redemption, resale, technical default and the establishment of a debt service fund). The results are shown in Table 6. Column (1) shows the results of the regression between D&O liability insurance and investment & financing contractual terms, with the regression coefficient of 0.864 and significant at the 1% level, indicating that creditors will demand more contractual terms to protect their rights and interests in order to prevent executives from making major investment decisions. The regression coefficient is 0.985 and significant at the 1% statistical level, indicating that creditors expect companies that purchase D&O liability insurance to make risky strategic decisions and therefore set more option-based contractual terms such as interest rate adjustment and risk default compensation to protect themselves.

The influence of D&O liability insurance on bond credit rating and bond maturity
This section further examines the impact of subscription to D&O liability insurance on the credit rating of the debt and the maturity of the bond. A bond credit rating is a rating that indicates the creditworthiness of a debtor by assessing the reliability of a particular bond issued by an independent legal entity in terms of its ability to meet its debt service obligations. D&O liability insurance has two main functions: external monitoring and governance and risk underwriting. Xiao and Liao (2007) found that the more serious the short-selling of a company by its majority shareholders, the weaker the protection of creditors and the shorter the maturity of the bond. In addition, by continuously monitoring the management's business decision-making activities, D&O liability insurance can prevent major mistakes in decision-making and improve the soundness of the company's operations. Moreover, due to the uncertainty in the course of business, even if a company faces the risk of not being able to repay its bonds, the Table 5. D&O liability insurance and pricing of corporate bonds: a cross-sectional analysis. Notes: The numbers in brackets are T values. ***, **, and * represent significance at 1%, 5%, and 10% levels, respectively. All standard errors have been adjusted for robustness.
risk underwriting function of the D&O liability insurance can provide some compensation in lieu of management, reducing the likelihood of the bonds not being repaid. Therefore, we expect bonds issued by companies subscribing to the D&O liability insurance to have a higher credit rating.
Referring to the processing methods of Chen and Li (2013), Lin, Officer et al. (2013), this paper assigns the bond credit rating AA-to 1, AA to 2, AA+ to 3, and AAA to 4, thus define the multivariate variable of Credit_rating(=1, 2, 3, 4) and uses the Ologit model to test. Bond maturity measured by Maturity. The regression results are shown in Table 7. The column (1) is the influence of D&O liability insurance on the bond credit rating. The coefficient of Ins is 0.778 and is significant at the level of 1%. The column (2) is the influence of D&O liability insurance on bond maturity. The coefficient of Ins is 0.238 and is significant at the level of 5%. The above results show that D&O liability insurance can play its role in supervision and governance, and effectively improve bond credit rating and bond maturity.

Robustness checks
This paper describes the effect of subscription to D&O liability insurance on bond issuance and its underlying mechanisms from the perspective of external monitoring. However, we argue that there may be a very different path to explain the phenomenon. For example, companies with better governance tend to choose D&O liability insurance, while such companies issue bonds with inherently higher credit ratings and lower credit spreads. Based on this, we conducted an endogeneity test to control for the effect of endogeneity on the conclusions of this paper.

Instrumental variable regression
Referring to Yuan et al. (2018), we select the overseas-experience of executives (Foreignexperience) as an instrumental variable for subscribing to D&O liability insurance. The takeup rate of D&O liability insurance among firms in mature capital markets exceeds 90%, and executives with overseas backgrounds have in-depth knowledge of the market mechanism of D&O liability insurance and are more willing to purchase D&O liability insurance as a risk hedging mechanism. At the same time, there is no literature showing that the overseas background of executives has a direct impact on the pricing of corporate bond issues, thus Foreign-experience satisfies the relevance and exogeneity requirements. The regression results are shown in Table 8, with column (1) reporting the correlation between the instrumental variable and the explanatory variable. The coefficient of Foreign is 0.632 and is statistically significant at the 1% level, suggesting that executives with an overseas background are more likely to subscribe to D&O liability insurance. Column (2) reports the regression results for the instrumental variables, with the regression coefficient on Ins and Creditspread being significantly negative at the 5% level, which remains consistent with the previous results.

Propensity score matching
Compared to foreign capital markets with a rate of over 97%, the purchase rate of D&O liability insurance for Chinese listed companies is lower, so it is likely that companies subscribing to D&O liability insurance have been screened out during the purchase process, leaving behind companies with inherently better corporate governance. Based on such a possibility, we used the propensity score matching method to control for the impact of differences in firm characteristics on the findings of this paper. Results remain robust after controlling for potential endogeneity issues. The conclusions will not be shown due to space limitations.

Heckman two-step method
Since the purchase of D&O liability insurance is non-random, then there may be a sample self-selection problem in the regression process, we use the Heckman two-step method to control for the impact of potential sample self-selection problems on the empirical results. Results remain robust after controlling for potential endogeneity issues. The conclusions will not be shown due to space limitations.

Conclusions
The corporate governance effect of D&O liability insurance is a hot topic in the field of corporate finance, and its practical role in corporate governance has been controversial due to the external monitoring effect and opportunistic effect, which has hindered the Notes: The numbers in brackets are T values ***, **, and * represent significance at 1%, 5%, and 10% levels, respectively. All standard errors are adjusted for robustness.
promotion and development of D&O liability insurance in China. This paper examines the role of D&O liability insurance in corporate governance from the perspective of bond market participants. The study finds that the purchase of D&O liability insurance can effectively reduce the pricing of bond issues, and the findings remain robust after controlling for potential endogeneity issues, including through the instrumental variables approach. Path tests suggest that the purchase of D&O liability insurance improves the quality of a company's internal controls as an important path for influencing bond issue pricing. Further research finds that the impact of D&O liability insurance on bond issue pricing is stronger when management has more power, poorer investor protection or higher financial risk; D&O liability insurance can play a corporate governance role, with creditors setting fewer governance-type contractual terms, but increasing investment and option-type contractual terms to constrain management's risky investment behaviour and protect their own interests; furthermore, companies that purchase D&O liability insurance issue bonds with higher credit ratings and longer maturities. This paper examines the impact of D&O liability insurance on the pricing of bond issues, taking the issuance of corporate bonds in China as an entry point. Theoretically, this paper analyses the corporate governance role of D&O liability insurance from the perspective of bond issue pricing. D&O liability insurance can exert external oversight and governance effects, improve the quality of a company's internal controls, inhibit management's self-interest and reduce the risk of bond defaults, thereby reducing bond issue pricing. Thus, this paper enriches the literature on the corporate governance effects of D&O liability insurance and broadening the study of factors influencing bond issue pricing. In practical terms, the research in this paper provides empirical evidence to promote effective pricing of bonds in the Chinese bond market. China's insistence on pursuing an independent innovation path with Chinese characteristics and implementing an innovation-driven development strategy cannot be achieved without the strong support of the capital market. Therefore, the stable development of the bond market is of paramount importance, which is related to stimulating the vitality of market players and promoting high-quality corporate development. The Fifth Plenary Session of the 19th CPC Central Committee proposed to improve the financing structure, vigorously develop the bond market and multi-level capital market, co-ordinate the planning of financial infrastructure and build a financial infrastructure management system that can adapt to Notes: The numbers in brackets are T values. ***, **, and * represent significance at 1%, 5%, and 10% levels, respectively. All standard errors have been adjusted for robustness.
the two-way opening of finance. Effective pricing of bonds plays a driving and leading role in promoting the smooth development of the bond market. In short, only when the bond pricing mechanism is continuously improved can the bond market vitality be continuously stimulated, thus promoting high-quality corporate development.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This study is funded by The National Natural