Pricing and hedging of derivatives based on non-tradable underlyings

Details Pricing and hedging of derivatives based on non-tradable underlyings Pricing and hedging of derivatives based on non-tradable underlyings

2007-12-21

arxiv.org/abs/0712.3746v1

Mathematical Finance, 2010, 20, 289 - 312

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

10.1111/j.1467-9965.2010.00398.x

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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