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Pricing and hedging of derivatives based on non-tradable underlyings

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  • Stefan Ankirchner
  • Peter Imkeller
  • Goncalo dos Reis

Abstract

This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable 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.

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  • Stefan Ankirchner & Peter Imkeller & Goncalo dos Reis, 2007. "Pricing and hedging of derivatives based on non-tradable underlyings," Papers 0712.3746, arXiv.org.
    • Handle: RePEc:arx:papers:0712.3746
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    File URL: http://arxiv.org/pdf/0712.3746
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    Cited by:

    1. Xavier De Scheemaekere, 2009. "Upper and lower bounds on dynamic risk indifference prices in incomplete markets," Papers 0909.3219, arXiv.org, revised Sep 2010.

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