Dissertation- – Multi-Asset Utility-Based Pricing and Hedging of Derivatives on Non-Traded Assets
In this report, the single-asset basis risk model is extended to a multi-asset version where multiple traded assets are used to price and hedge a derivative on a non-traded asset. This was done for the exponential utility function both in the case where the agent is assumed to have knowledge of the asset price drifts (the full information setting) and the case where the agent is assumed to be uncertain about the values of these drifts (the partial information setting). Through altering approach, the partial information model was converted to an effective full information model with random drifts that are adapted to the observation filtration generated by the asset prices. In both the cases with full and partial information, an analytic formula for the optimal hedge and a PDE for the utility indifference price have been obtained. In addition, an analytic solution has been derived for the utility indifference price in the full information setting and it was shown that a mutual fund result holds in the full information but not in the partial information setting.
Through power series expansions of the utility indifference price and hedge and a marginal price approximation to the utility indifference price, the unfiltered and the filtered utility- based hedging strategies were respectively implemented. The results indicate that if multiple assets are used for utility-based hedging, the hedge performance is significantly improved through a reduction in the standard deviation and range of the terminal hedging error distributions.
