Valuing GWBs with Stochastic Interest Rates and Volatility

Donnelly, Ryan Francis, Sebastian Jaimungal, and Dmitri Rubisov. "Valuing GWBs with stochastic interest rates and volatility." Quantitative Finance (2012).

26 Pages Posted: 14 Jan 2012 Last revised: 27 Apr 2015

See all articles by Ryan Francis Donnelly

Ryan Francis Donnelly

University of Washington - Department of Applied Mathematics

Sebastian Jaimungal

University of Toronto - Department of Statistics

Dmitri Rubisov

BMO Capital Markets

Date Written: January 13, 2012

Abstract

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.

Keywords: Insurance Guarantees, Withdrawal Benefits, Stochastic Volatility, Stochastic Interest Rates, ADI methods, Asian Options, Mixed Fund

JEL Classification: G12, G13, C63

Suggested Citation

Donnelly, Ryan Francis and Jaimungal, Sebastian and Rubisov, Dmitri, Valuing GWBs with Stochastic Interest Rates and Volatility (January 13, 2012). Donnelly, Ryan Francis, Sebastian Jaimungal, and Dmitri Rubisov. "Valuing GWBs with stochastic interest rates and volatility." Quantitative Finance (2012).. Available at SSRN: https://ssrn.com/abstract=1984885 or http://dx.doi.org/10.2139/ssrn.1984885

Ryan Francis Donnelly

University of Washington - Department of Applied Mathematics ( email )

Box 352420
Seattle, WA 98195-2420
United States

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

Dmitri Rubisov

BMO Capital Markets ( email )

Canada

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