Valuation Of Claims On Nontraded Assets Using Utility Maximization
AbstractA 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. Copyright 2002 Blackwell Publishers.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 12 (2002)
Issue (Month): 4 ()
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Feb 2012.
- Marcelo J. Villena & Axel A. Araneda, 2014. "Option Pricing of Twin Assets," Papers 1401.6735, arXiv.org.
- Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1606-1620, November.
- Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497, arXiv.org, revised Oct 2013.
- Hardy Hulley & T. A. McWalter, 2008. "Quadratic Hedging of Basis Risk," Research Paper Series 225, Quantitative Finance Research Centre, University of Technology, Sydney.
- Mingxin Xu, 2004.
"Risk Measure Pricing and Hedging in Incomplete Markets,"
0406004, EconWPA, revised 06 Apr 2005.
- Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
- Eduardo S. Schwartz & Claudio Tebaldi, 2006. "Illiquid Assets and Optimal Portfolio Choice," NBER Working Papers 12633, National Bureau of Economic Research, Inc.
- Mitja Stadje & Antoon Pelsser, 2011. "Time-Consistent and Market-Consistent Evaluations," Papers 1109.1749, arXiv.org, revised Dec 2013.
- Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
- Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
- David German, 2010. "Overview of utility-based valuation," Papers 1003.5712, arXiv.org.
- Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
- Giuseppe Benedetti & Luciano Campi, 2013. "Utility indifference valuation for non-smooth payoffs with an application to power derivatives," Papers 1307.4591, arXiv.org.
- Siddiqi, Hammad, 2013. "Mental Accounting: A Closed-Form Alternative to the Black Scholes Model," MPRA Paper 50759, University Library of Munich, Germany.
- Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
- Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
- Stefan Ankirchner & Gregor Heyne, 2012. "Cross hedging with stochastic correlation," Finance and Stochastics, Springer, vol. 16(1), pages 17-43, January.
- Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
- Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
- Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
- Jan Kallsen & Shen Li, 2013. "Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach," Papers 1309.3479, arXiv.org.
- Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.