VALUATION OF CLAIMS ON NONTRADED ASSETS USING UTILITY MAXIMIZATION

Authors


  • The author thanks David Hobson for many helpful conversations, and Rafal Wojakowski and Glenn Kentwell for useful comments. Thanks also go to seminar participants at ETH Zurich, at Kings' College London, Lancaster, and Bath, and at the 5th Annual conference on Real Options UCLA, the 14th Annual FORC conference, and RISK Math Week London.

Address correspondence to the author at Nomura Centre for Quantitative Finance, Mathematical Institute, 24–29 St. Giles', Oxford, 0x1 3LB, UK; e-mail: hendersl@maths.ox.ac.uk.

Abstract

A topical problem is how to price and hedge claims on nontraded assets. A natural approach is to use for hedging purposes another similar asset or index which is traded. To model this situation, we introduce a second nontraded log Brownian asset into the well-known Merton investment model with power law and exponential utilities. The investor has an option on units of the nontraded asset and the question is how to price and hedge this random payoff. The presence of the second Brownian motion means that we are in the situation of incomplete markets. Employing utility maximization and duality methods we obtain a series approximation to the optimal hedge and reservation price using the power utility. The problem is simpler for the exponential utility, and in this case we derive an explicit representation for the price. Price and hedging strategy are computed for some example options and the results for the utilities are compared.

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