Actuarial Transform Pricing

32 Pages Posted: 3 Apr 2010

See all articles by Oleg A. Ruban

Oleg A. Ruban


Luiz Vitiello

University of Essex - Essex Business School

Ser-Huang Poon

Alliance Manchester Business School, University of Manchester; Alan Turing Institute

Multiple version iconThere are 2 versions of this paper

Date Written: January 30, 2010


This article studies four transform pricing methods in the context of general equilbrium (GE) framework. The four methods, viz. the Esscher transform, indifference pricing, the Wang transform, and the standard deviation loading, are popular among actuarial literature and practice. The transform pricing methods offer a convenient solution to contingent claim pricing problem with the underlying risk exposure cannot be fully hedged. We show analytically that these four methods are similar and close to the GE approach if the utility has an exponential function, and the underlying distribution is Normal. When the payoff distribution is non-gaussian, prices produced by the four methods vary widely. Moreover, some transform methods may lead to prices that are not coherent, violating one or more of the following properties, additivity, homogeneity, scale invariance and monotonicity. We discuss the implications of our findings on incomplete market pricing.

Keywords: Esscher transform, indifference pricing, Wang transform, standard deviation loading

JEL Classification: D52, G13, C22

Suggested Citation

Ruban, Oleg A. and Vitiello, Luiz and Poon, Ser-Huang, Actuarial Transform Pricing (January 30, 2010). Manchester Business School Research Paper No. 592, Available at SSRN: or

Oleg A. Ruban

MSCI Inc. ( email )

88 Pine Street
2nd Floor
New York, NY 10005
United States

Luiz Vitiello

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

Ser-Huang Poon (Contact Author)

Alliance Manchester Business School, University of Manchester ( email )

Alliance Manchester Business School
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Manchester, Manchester M15 6PB
United Kingdom
+44 161 275 4031 (Phone)
+44 161 275 4023 (Fax)


Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

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