Closed-Form Solutions for Guaranteed Minimum Accumulation Benefits

40 Pages Posted: 19 Apr 2014

See all articles by Mikhail Krayzler

Mikhail Krayzler

Technische Universität München (TUM) - Chair of Mathematical Finance

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance

Bernhard Brunner

University of Augsburg - Department of Finance and Banking

Date Written: November 30, 2012

Abstract

Guaranteed Minimum Accumulation Benefit (GMAB) is one of the variable annuity products, i.e. new type of insurance and retirement products offering participation at the financial markets and the guarantees at the same time. In particular, GMAB offers at maturity the maximum of account value and some guaranteed benefit. This paper considers four most popular options for this guaranteed amount: capital protection, minimum interest return, ratchet and the maximum of them. As these products are exposed to different risk factors, a multi-factor model is required. However, there is often a tradeoff between a realistic model and analytical tractability. Thus, some authors simplify the contract setup or/and the modeling framework to derive closed-form solutions, others use different numerical methods to price the guarantees. This work fills this gap by providing analytical formulas for GMAB with common riders in a hybrid model for actuarial and financial risks.

Keywords: Variable Annuities, Guaranteed Minimum Accumulation Benefit, Hybrid Model

JEL Classification: G12, G13, G22, G23

Suggested Citation

Krayzler, Mikhail and Zagst, Rudi and Brunner, Bernhard, Closed-Form Solutions for Guaranteed Minimum Accumulation Benefits (November 30, 2012). Available at SSRN: https://ssrn.com/abstract=2425801

Mikhail Krayzler (Contact Author)

Technische Universität München (TUM) - Chair of Mathematical Finance ( email )

Parkring 11
Garching-Hochbrück, 85748
Germany

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance ( email )

Parkring 11
Garching-Hochbrueck, 85748
Germany
+49 89 289 17400 (Phone)

Bernhard Brunner

University of Augsburg - Department of Finance and Banking ( email )

Universitaetsstr. 2
Augsburg, 86135
Germany

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