Delta Hedging Variable Annuities under Wiener Chaos Expansion
Abstract
We present a method for Delta-Hedging of variable annuity products under the Guaranteed Minimum withdrawal Benefit (GMWB) Rider based on Wiener Chaos expansion. We also discuss well-known Monte-Carlo methods for computing Delta for derivatives, particularly for variable annuities. A detailed discussion of Wiener Chaos expansion is then provided. A discussion on the Heath-Jarrow-Morton (HJM) framework in the context of constant and exponential volatility is given. Choosing a Geometric Brownian motion for the underlying in the variable annuity account and the Heath-Jarrow-Morton model for interest rates we present results of delta computed by the Wiener Chaos technique in MATLAB using the UQLab framework. Comparisons between this method and the Monte-Carlo benchmark are then presented.
Description
Keywords
Mathematics
Citation
Wiredu, D. (2017). Delta Hedging Variable Annuities under Wiener Chaos Expansion (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25545