The main task in this essay entails modeling a finite sequence of forward Euribor interest rates as continuous-time stochastic processes under several equivalent martingale probability measures, and in particular, under the terminal measure. To achieve this, we consider a continuous trading economy that is free from arbitrage, and further proceed to implement a Monte Carlo method for pricing interest rate derivatives such as caps and caplets within these forward Euribor rate processes. We briefly review tools for stochastic differential equations and use this knowledge to construct the equation describing the dynamics of the Euribor market model, wherein prices of trading assets become martingales.
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