Yield curve modeling is a fundamental concept in finance, playing a crucial role in understanding the relationship between interest rates and time. G2++ is a popular interest rate model used for this purpose, an improved version of the original Hull-White model. In this work, we describe the two Gaussian interest rate models (G2++) where the instantaneous short rate “r” is the sum of two correlated stochastic processes plus a deterministic function. We assume that each of these processes has a Gaussian distribution with time-dependent volatility. The deterministic function is determined by exact fitting to observed term structures. We test the model through various numerical experiments to assess its goodness of fit to yield curves with different maturities quoted in the market. Additionally, we analyze the errors between the model and the initial yield after a time lapse. Overall, implementing G2++ for yield curve modeling can provide a powerful tool for analyzing and managing interest rate risk in financial markets.
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