Pricing and Hedging of Derivatives Based on Nontradable Underlyings

24 Pages Posted: 29 Mar 2010

See all articles by Stefan Ankirchner

Stefan Ankirchner

University of Bonn

Peter Imkeller

Humboldt University of Berlin - Department of Mathematics

Gonçalo Dos Reis

affiliation not provided to SSRN

Date Written: 2008-05

Abstract

This paper is concerned with the study of insurance related derivatives on financial markets that are based on nontradable underlyings, but are correlated with tradable assets. We calculate exponential utility-based indifference prices, and corresponding derivative hedges. We use the fact that they can be represented in terms of solutions of forward-backward stochastic differential equations (FBSDE) with quadratic growth generators. We derive the Markov property of such FBSDE and generalize results on the differentiability relative to the initial value of their forward components. In this case the optimal hedge can be represented by the price gradient multiplied with the correlation coefficient. This way we obtain a generalization of the classical “delta hedge” in complete markets.

Suggested Citation

Ankirchner, Stefan and Imkeller, Peter and Reis, Gonçalo Dos, Pricing and Hedging of Derivatives Based on Nontradable Underlyings (2008-05). Mathematical Finance, Vol. 20, Issue 2, pp. 289-312, April 2010, Available at SSRN: https://ssrn.com/abstract=1578538 or http://dx.doi.org/10.1111/j.1467-9965.2010.00398.x

Stefan Ankirchner (Contact Author)

University of Bonn ( email )

Regina-Pacis-Weg 3
Postfach 2220
Bonn, D-53012
Germany

Peter Imkeller

Humboldt University of Berlin - Department of Mathematics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Gonçalo Dos Reis

affiliation not provided to SSRN

No Address Available

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