THE LIMITATIONS OF NO-ARBITRAGE ARGUMENTS FOR REAL OPTIONS

F. Hubalek () and W. Schachermayer ()
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F. Hubalek: Department of Statistics, Probability Theory and Actuarial Mathematics (107/5), Vienna University of Technology, Wiedner Hauptstr. 8–10, A–1040 Wien, Austria
W. Schachermayer: Department of Statistics, Probability Theory and Actuarial Mathematics (107/5), Vienna University of Technology, Wiedner Hauptstr. 8–10, A–1040 Wien, Austria

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 02, 361-373

Abstract: We consider an optioncwhich is contingent on an underlying$\tilde S$that is not a traded asset. This situation typically arises in the context of real options. We investigate the situation when there is a "surrogate" traded assetSwhose price process is highly correlated with that of$\tilde S$. An illustration would be the cases whereSand$\tilde S$model two different brands of crude oil. The main result of the paper shows that in this case one cannot draw any non-trivial conclusions on the price of the option by only using no-arbitrage arguments.In a second step we try to isolate hedging strategies on the traded assetSwhich minimize the variance of the hedging error. We show in particular, that the naive strategy of simply replacing$\tilde SbySfails to be optimal and we are able to quantify how far it is from being optimal.

Keywords: Arbitrage pricing theory; real options; correlated Brownian motions; variance-optimal hedging (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901001024

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