基于信息的方法：存在违约时间时信用风险资产的定价
Information-Based Approach: Pricing of a Credit Risky Asset in the Presence of Default Time
AI总结：
本研究扩展基于信息的资产定价框架，纳入发行方随机违约时间，推导信用风险资产及期权价格，证明相关停时的完全不可达性，适用于违约不可预测的金融市场场景。
摘要：
我们对Brody、Hughston与Macrina提出的基于信息的资产定价框架进行扩展，纳入资产发行方的随机破产时间。本模型引入了将在时刻T支付的无违约现金流$Z_T$，同时资产发行方的可能破产时刻$τ$与长度为$ν=τ\bigwedge T$、钉住点为$σZ_T$的布朗随机桥（其中$σ$为常数）生成的滤子相一致。变量$Z_T$与$τ$不一定相互独立，模型并不严格依赖将$τ$解释为破产时间的设定。我们推导了该资产的价格过程，并计算了相关期权的价格，价格过程的动力学满足扩散方程。采用P.-A. Meyer的方法，我们给出了$ν$的补偿子的显式计算结果。利用桥过程的特殊性质，我们还给出了$Z_T\mathbb{I}_{[ν,+\infty)}$的补偿子的显式表达式。所得结论凸显了停时$ν$的完全不可达性质，这一特征尤其适用于金融市场——在违约发生前，无法通过系统内的任何其他信号预测发行方的违约时间。
英文摘要：
We extend the information-based asset-pricing framework by Brody, Hughston \& Macrina to incorporate a stochastic bankruptcy time for the writer of the asset. Our model introduces a non-defaultable cash flow $Z_T$ to be made at time $T$, alongside the time $τ$ of a possible bankruptcy of the writer of the asset are in line with the filtration generated by a Brownian random bridge with length $ν=τ\wedge T$ and pinning point $σZ_T$, where $σ$ is a constant. Quantities $Z_T$ and $τ$ are not necessarily independent. The model does not depend crucially on the interpretation of $τ$ as a bankruptcy time. We derived the price process of the asset and compute the prices of associated options. The dynamics of the price process satisfy a diffusion equation. Employing the approach of P.-A.~ Meyer, we provide the explicit computation of the compensator of $ν$. Leveraging special properties of the bridge process, we also provide the explicit expression of the compensator of $Z_T\,\mathbb{I}_{[ν,+\infty)}$. The resulting conclusion highlights the totally inaccessible property of the stopping time $ν$. This characteristic is particularly suitable for financial markets where the time of default of a writer cannot be predictable from any other signal in the system until default happens.
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