科技金融中证券设计模型及数理分析

本文聚焦中小微企业融资约束问题，运用经济学理论和数学方法研究中小微企业融资过程中的新型融资模式及其证券合约设计。在信息不对称条件下分别分析了新型担保互换、证券代币发行等模式，并给出了贝叶斯均衡分析及最优合约设计；在两状态的马尔科夫链区制变换框架下分析了有政府补贴的信用担保及最优担保补贴问题。在私募股权基金资产证券化过程中给出了公司证券定价及证券合约设计。本文从不对称信息、外部性以及流动性缺失等市场缺陷出发，围绕多元化的融资模式创新与证券设计，分别根据离散单周期模型和连续时间模型给出了均衡状态下的定价分析，并通过比较静态分析、蒙特卡洛模拟等数值方法给出了经济学解释和相关政策建议。本文贡献总结如下：    
    
考虑信息不对称，本文建立一个具有信用担保互换的单周期投资模型，包括担保换费用（Fee-for-Guarantee swaps，FGS）、担保换股权（Equity-for-Guarantee swaps，EGS）和担保换期权（Option-for-Guarantee swaps，OGS）。企业家是风险厌恶的，存在两种类型，优质企业容易遭受逆向选择问题带来的影响。研究表明，在混同均衡中，高质量企业被迫将部分利润转移给低质量企业。即使在分离均衡下，高质量企业也有可能遭受逆向选择的损失。对于优质企业而言，OGS融资模式是最好的，且更容易达到分离均衡。当担保成本可行时，期权的行权价格越高，项目价值越高，最优行权价格是使得担保成本达到其最大时的价格。
    
考虑信息不对称和持股质量信号，本文解决了证券代币发行（Security token offerings，STO）的最优证券设计问题。企业家是风险厌恶的，我们比较证券代币发行和贷款担保两种融资模式。研究表明，在信息对称情况下，STO优于贷款担保。在信息不对称情况下，我们识别出促使低质量创业者模仿无利可图的最高股权价格。研究发现，当项目风险足够高时，通过贷款担保可以达到混同均衡，而通过STO融资则可以达到分离均衡；反之，则相反的结论成立。我们模型解释了，如果项目风险较低或者创业者风险厌恶程度较弱，那么贷款担保要优于STO；反之，STO则作为一种金融创新，相对于贷款担保具有显著优势。
  
考虑企业发展的外部溢出效应，本文在两状态的马尔科夫链区制转换模型下研究了信用担保和政府补助对投资的影响。假设项目现金流是由布朗运动和两状态的马尔科夫链驱动的，我们为一般的标准资产提供了解析定价公式，大多数公司证券可以通过该定价公式得到精确计算。结果表明，在经济繁荣时期的时间越长，投资加快，担保费率将会越低。在考虑公司外部性下，政府补贴加快了企业投资。我们确定了激励企业家立即投资所需要的补贴金额，并通过政府补贴研究了最优资本结构。直接投资所需的政府补贴不仅取决于当前现金流水平还取决于经济区制状态。我们的研究结果有助于解决如何根据项目外部性采取有效激励或抑制投资等问题，其基本思想与ESG（Environment, social and governance）投资理念一致。

考虑政府引导基金流动性问题，本文研究了担保基金凭证（Collateralized fund obligations，CFO）的资产证券化产品定价问题。投资于中小微企业的政府引导基金由于流动性、时间错配等原因难以及时退出，这为基金的可持续运营和资金流动性带来了障碍。将资产池内的现金流进行打包，按照不同的收益优先级进行分配。研究表明，担保基金凭证在特质性风险方面具有风险分散效应，还可以有效缓解基金流动性问题。我们给出了资产证券化产品的定价分析，这为基金可持续运营以及中小微企业融资提供了理论参考。

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