Averaged Index Ratio State-Space Model and Kalman Filtering

A theoretical model describing joint dynamics of a spot Index (e.g. Libor), an Averaged Index (e.g. BMA) and the respective ratio is suggested. A convolution‐like “coupling” between the two indices is introduced. The model is represented as a system of stochastic algebraic and differential equations. The Kalman Filter technique is proposed as a tool to calibrate the model. Transition from real world to risk‐neutral measure is considered. An example of calibration based on recently observed market rates is provided. A Kalman Filter‐based hedging is discussed.