Valuing GWBs with Stochastic Interest Rates and Volatility
University of Toronto - Department of Statistics
University of Toronto - Department of Mathematics
BMO Capital Markets
January 13, 2012
Guaranteed withdrawal benefits (GWBs) are long term contracts which provide investors with equity participation while guaranteeing them a secured income stream. Due to the long investment horizons involved, stochastic volatility and stochastic interest rates are important factors to include in their valuation. Moreover, investors are typically allowed to participate in a mixed fund composed of both equity and fixed-income securities. Here, we develop an efficient method for valuing these path-dependent products through re-writing the problem in the form of an Asian styled claim and a dimensionally reduced PDE. The PDE is then solved using an Alternating Direction Implicit (ADI) method. Furthermore, we derive an analytical closed form approximation and compare this approximation with the PDE results and find excellent agreement. We illustrate the various effects of the parameters on the valuation through numerical experiments and discuss their financial implications.
Number of Pages in PDF File: 23
Keywords: Insurance Guarantees, Withdrawal Benefits, Stochastic Volatility, Stochastic Interest Rates, ADI methods, Asian Options, Mixed Fund
JEL Classification: G12, G13, C63working papers series
Date posted: January 14, 2012 ; Last revised: January 19, 2012
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo6 in 0.344 seconds