Utility based pricing of contingent claims
AbstractIn a discrete setting, we develop a model for pricing a contingent claim. Since the presence of hedging opportunities influences the price of a contingent claim, first we introduce the optimal hedging strategy assuming a contingent claim has been issued: a strategy implemented by investing the budget plus the selling price is optimal if it maximizes the expected utility of the agent's revenue, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the `reservation price' as a subjective valuation of a contingent claim. This is defined as the minimum price to be added to the initial budget that makes the issue of the claim more preferable than optimally investing in the available securities. We define the reservation price both for a short position (reservation selling price) and for a long position (reservation buying price) in the contingent claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu price. We develop a numerical procedure to evaluate the reservation price and two applications are provided. Different utility functions are used and some qualitative properties of the reservation price are shown.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 9902003.
Length: 30 pages
Date of creation: 08 Feb 1999
Date of revision: 14 Oct 2002
Note: Type of Document - LaTex; prepared on Mac; to print on PostScript; pages: 30; figures: included
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Incomplete markets; reservation price; expected utility; optimization;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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CEMAPRE Working Papers
1103, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
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