Forward Measures: Interest Rate Models

This lecture covers the concept of forward measures in interest rate models, where bond price processes are discounted by different measures. It explains the 'change of numeraire' technique for option pricing and derives closed-form bond option price formulas for Gaussian HJM models. The lecture also discusses the setup of a filtered probability space, the definition of T-forward measures, and their application in derivatives pricing. Additionally, it explores the fundamental property of bond price processes and the dynamics of forward rates in the HJM framework. The lecture concludes with bond option pricing, put-call parity, and an example using the Vasiček short rate model.