Brooklyn Quant Experience Lecture Series - Fourier-Based Methods for Complex Insurance Products Management

Explore Fourier-based methods for managing complex insurance products in this lecture by Laura Ballotta, Reader in Financial Mathematics at Cass Business School. Delve into the intricacies of Variable Annuity Contracts, focusing on the Ratchet design and its valuation. Learn about surrender models, mortality risk models, and fair market value calculations. Discover the application of Fourier transform techniques in derivatives valuation, specifically for Guaranteed Minimum Accumulation Benefits (GMAB) and Surrender Benefits. Examine integration methods in high dimensions and analyze numerical experiments, including parameter settings and importance sampling distributions. Gain insights into sensitivity analysis and explore a general framework for market modeling in the context of complex insurance products.

Introduction
The Variable Annuity Contract
Agenda
Variable Annuity - the Ratchet design (1)
Surrender model
Mortality risk model
Valuation: Fair Market Value
Fourier transform for derivatives valuation
Value of the GMAB
Value of the Surrender Benefit
Integration in high dimensions
Numerical experiment setup
Parameters and importance sampling distribution
Results
Sensitivity analysis
Conclusions
Market model: a general framework