The Application of Calculus in Credit Default Swaps: Pricing, Risk Assessment, and Market Implications

Abstract

This paper aims at the investigation of one of the derivatives, namely from the group of Credit Default Swaps, with the help of calculus and, more particularly, differential equations and integrals. The plan is to show how these calculative instruments may be utilized to price and risk measure CDS and to thereby illustrate the utility of such models in mitigating financial risks. The paper is structured as follows: In Section 2, ‘The mechanics and functionality of CDS’, the focus is brought on the specifics of construction of CDS contracts, and the matter of their pricing. Valuation of CDS is described in section three where differential equations and integrals are used in the mathematical modeling of these instruments. Section 4 also focuses on the connection between CDS and market stability; this section also looks at the positive and negative effects of CDS on the financial markets. Finally, Section 5 provides conclusion and recommendation for the subsequent research.