Interest rates fluctuate over time, causing risks for both creditors and debtors. For a more precise analysis of this risk, we need to present an economic structure using a mathematical model. In our work, we have chosen a model that does not allow arbitrage. Firstly, we analyze various types of interest rates in general and determine their behavior within the given model. We also explore the different types of compounding and place the continuous compounding, discussed until then, into context. In the essential part, when dealing with financial instruments for managing the risks brought about by interest rates, we use simple compounding for easier representation. Through examples, we examine agreements on interest rates, swaps, and various types of swaptions. We provide a more detailed mathematical description of cap and floor swaps.
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