An economic scenario generator for embedded derivatives in South Africa
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Date
Authors
Levendis, Alexis Jacques
Mare, Eben
Journal Title
Journal ISSN
Volume Title
Publisher
Actuarial Society of South Africa
Abstract
It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims.
The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest
rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a
Hull-White short rate process and can be combined with the Heston stochastic volatility model to form
the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between
the equity and interest rate processes, a component that is important when pricing long-dated contingent
claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity
Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance
industry in South Africa. We propose a further extension by including stochastic mortality rates based
on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1)
model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for
GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of
embedded derivative liabilities.
Description
Keywords
Heston-Hull-White, Stochastic volatility, Stochastic interest rates, Stochastic mortality, Pricing, Hedging, Guaranteed minimum death benefit (GMDB), Guaranteed minimum maturity benefit (GMMB)
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Citation
Levendis, A. & Mare, E. 2022, 'An economic scenario generator for embedded derivatives in South Africa', South African Actuarial Journal, vol. 22, pp. 79-118. DOI; 10.4314/saaj.v22i1.4