PRICING AND HEDGING OF DERIVATIVES BASED ON NONTRADABLE UNDERLYINGS

Stefan Ankirchner, Peter Imkeller*, Goncalo Dos Reis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)289-312
Number of pages24
JournalMathematical Finance
Volume20
Issue number2
DOIs
Publication statusPublished - Apr 2010

Keywords

  • financial derivatives
  • hedging
  • utility-based pricing
  • BSDE
  • forward-backward stochastic differential equation (FBSDE)
  • quadratic growth
  • differentiability
  • stochastic calculus of variations
  • Malliavin calculus
  • pricing by marginal utility
  • STOCHASTIC DIFFERENTIAL-EQUATIONS
  • UTILITY MAXIMIZATION
  • QUADRATIC GROWTH
  • OPTIONS
  • BSDES
  • RISK

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