Filtering Prediction and Robust Estimation for a Jump-Integrated ARIMA Model and Q-Forward Pricing

This thesis introduces an ARIMA(p, d, 0)-J model for q-forward pricing, incorporating jump dynamics into mortality modeling. A filtering prediction algorithm combined with Huber M-estimation detects and adjusts for jumps, improving parameter stability and accuracy. Jump occurrences are modelled via a compound binary Markov process with distributed jump sizes. Simulation results show superior performance over OLS and robust linear models in bias, mean squared error, and jump detection, especially under negative correlation. Empirical application reveals that jump-inclusive models yield higher q-forward rates, reflecting elevated mortality risk and increased premiums when market risk prices become more negative.