Abstract
Swap is a financial contract between two counterparties who agree to exchange one cash flow stream for another, according to some predetermined rules. When the cash flows are fixed rate interest and floating rate interest, the swap is called an interest rate swap. This paper investigates two valuation models of the interest rate swap contracts in the uncertain financial market. The new models are based on belief degrees, and require relatively less historical data compared to the traditional probability models. The first valuation model is designed for a mean-reversion term structure, while the second is designed for a term structure with hump effect. Explicit solutions are developed by using the Yao–Chen formula. Moreover, a numerical method is designed to calculate the value of the interest rate swap alternatively. Finally, two examples are given to show their applications and comparisons.
Highlights
Interest rate swap is one of the most popular interest derivatives
In order to hedge this kind of risk, they decide to sign an interest rate swap contract
This paper mainly studied interest swap contracts in an uncertain financial market
Summary
Interest rate swap is one of the most popular interest derivatives. The interest rate swap began trading in 1981, and owns a hundred billion dollar market. Chen [15] studied a special type of multi-dimensional uncertain differential equation called a nested uncertain differential equation He extended the interest rate models to multi-factor term structure models. We assume that the floating interest rate follows a mean-reversion one-dimensional uncertain differential equation, and give the explicit solution of the interest rate swap. Considering the hump effect of the term structure, we assume that the floating interest rate follows a nested-uncertain differential equation, and derive explicit solutions of interest rate swap. We gave the valuation model wherein the floating interest rate follows a mean-reversion uncertain differential equation. We gave the valuation model wherein the floating interest rate follows a nested uncertain differential equation. We designed a numerical method to calculate the value of the interest rate swap, and give two examples to show the applications
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