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I am currently in the process of developing an interest rate model that would be used to price mortgage-backed securities and develop an OAS estimate. Referring to Brigo and Mercurio (2006) I'm focusing on two-factor models instead of one-factor to overcome the 'basic' assumption that all rates on the term structure are perfectly correlated. This is because, for this model, I need to simulate a short-rate (one month term) for points in time but also have an additional estimate of a longer-term rate (7 year or 10 year for example) for the purposes of knowing refinance rates at any given point in time. My first question: Is the G2++ model a suitable/realistic choice when one wants needs to estimate the term structure of interest rates at any point in time in the future? If not, what should I focus my time on learning and implementing?

The book I have referencing outlines a tree-based model but I am looking to ultimately create path simulations of future rates. At this point, I'm assuming it would be possible to sample paths from a calibrated tree but I am not familiar with quadrinomial trees (what the book outlines for the model) and how long such a calibration process would realistically take if one is trying to simulate paths of monthly rates for 5-15 years. From this, my second question is: Is there a source online you would recommend for a clear explanation of monte-carlo using G2++?

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