The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty
AbstractThe fact that the expected payoffs on assets and call options are infinite under most log-stable distributions led Paul Samuelson and Robert Merton to conjecture that assets and derivatives could not be reasonably priced under these distributions, despite their many other attractive features. This paper demonstrates that when the observed distribution of future prices is log-stable, the Risk Neutral Measure (RNM) under which asset and derivative prices may be computed as expectations is not itself log-stable in the problematic cases. Instead, the RNM is determined by the convolution of two densities, one negatively skewed stable, and the other an exponentially tilted positively skewed stable. The resulting RNM gives finite expected payoffs, and therefore demonstrates that these fears were in fact unfounded. Carr and Madan (1999) have shown how the Fast Fourier Transform (FFT) can be used to quickly evaluate options directly from the characteristic function of any RNM. The log-stable RNM characteristic function presented here therefore greatly facilitates the pricing of options on log-stable assets, by means of this new methodology, provided a Romberg adaptation of the FFT is employed. The full paper is at .
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Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 428.
Date of creation: 11 Aug 2004
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Stable distributions; risk-neutral measure; pricing kernel; option pricing; FFT; Romberg FFT;
Other versions of this item:
- J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics.
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-08-16 (All new papers)
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