A Dynamic Systems Perspective on Credit Risk Transfer Bonds Pricing: Insights from Black-Scholes PDE Analysis
Keywords:
Dynamic System, , Black Scholes PDE, , Credit Risk Derivative, , Credit Risk Transfer, , Credit Risk Transfer BondAbstract
This study delves into the dynamic systems paradigm applied to Black-Scholes partial differential equations (PDEs) and examines its efficacy in pricing credit risk derivatives. The Black-Scholes PDE is a cornerstone in financial research for pricing various instruments. However, the intricacies inherent in many financial scenarios often preclude the derivation of closed-form solutions, necessitating recourse to numerical methods for solutions. In response to this challenge, our paper proposes a novel approach leveraging dynamic systems derived from a semi-discretization technique applied to the price variable within the Black-Scholes PDE framework. Our focus extends to the realm of credit risk transfer bonds, a derivative instrument designed to reallocate credit risk from a financial institution to a risk buyer or investor. By delineating the structural characteristics of these bonds, we construct a PDE analogous to the Black-Scholes equation to capture the pricing dynamics inherent in such instruments. Subsequently, we employ the dynamic systems technique to solve the credit risk transfer bond PDE, thereby facilitating a comprehensive examination of the pricing dynamics involved. The application of this methodology is demonstrated through the utilization of PYTHON software, which enables the visualization and analysis of the obtained results. By bridging the gap between dynamic systems theory and financial derivatives pricing, this research contributes to advancing computational finance methodologies and offers insights into the pricing mechanisms of credit risk transfer bonds within a dynamic systems framework.
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