Bounds for Present Value Functions with Stochastic Interest Rates And Stochastic Volatility

24 Pages Posted: 2 Mar 2006

See all articles by Ann De Schepper

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Jan Dhaene

Katholieke Universiteit Leuven

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

David Vyncke

Ghent University - Department of Applied Mathematics and Computer Science

Abstract

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution.

In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds.

Suggested Citation

De Schepper, Ann and Goovaerts, Marc and Dhaene, Jan and Kaas, Rob and Vyncke, David, Bounds for Present Value Functions with Stochastic Interest Rates And Stochastic Volatility. Insurance: Mathematics and Economics, Vol. 31, No. 1, pp. 87-103, 2002 , Available at SSRN: https://ssrn.com/abstract=886309

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Jan Dhaene (Contact Author)

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

David Vyncke

Ghent University - Department of Applied Mathematics and Computer Science ( email )

Gent, 9000
Belgium

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