The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty

J. Huston McCulloch

No 428, Econometric Society 2004 North American Winter Meetings from Econometric Society

Abstract: The 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 .

Keywords: Stable distributions; risk-neutral measure; pricing kernel; option pricing; FFT; Romberg FFT (search for similar items in EconPapers)
JEL-codes: D81 G13 (search for similar items in EconPapers)
Date: 2004-08-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:ecm:nawm04:428

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