具有非时齐马氏过程的热核利率模型
Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes
摘要：
我们考虑一个热核方法的发展随机定价内核。核由正传播子构造，正传播子由时间非齐次马尔可夫过程驱动。我们将这样的传播子与一个正的、依赖于时间的、递减的权重函数相乘，并将乘积随时间积分。其结果是一个所谓的加权热核，通过建设是一个上鞅的时间非齐次马尔可夫过程所产生的过滤。作为一个应用程序，我们展示了这个框架如何自然地适合基于信息的资产定价框架，其中时间非齐次马尔可夫过程被用来模拟随机经济因素的部分信息。我们提出的例子，导致债券价格的分析公式，以及明确的表达相关的利率和市场价格的风险的定价核模型。此外，我们还在这个框架内解决固定收益衍生品的定价问题。
英文摘要：
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over time. The result is a so-called weighted heat kernel that by construction is a supermartingale with respect to the filtration generated by the time-inhomogeneous Markov processes. As an application, we show how this framework naturally fits the information-based asset pricing framework where time-inhomogeneous Markov processes are utilized to model partial information about random economic factors. We present examples of pricing kernel models which lead to analytical formulae for bond prices along with explicit expressions for the associated interest rate and market price of risk. Furthermore, we also address the pricing of fixed-income derivatives within this framework.
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