Abstract
This article constructs an entropy pricing framework by incorporating a set of informative risk-neutral moments (RNMs) extracted from the market-available options as constraints. Within the RNM-constrained entropic framework, a unique distribution close enough to the correct one is obtained, and its risk-neutrality is deeply verified based on simulations. Using this resultant risk-neutral distribution (RND), a sample of risk-neutral paths of the underlying price is generated and ultimately the European option’s prices are computed. The pricing performance and analysis in simulations demonstrate that this proposed valuation is comparable to the benchmarks and can produce fairly accurate prices for options.
Highlights
The key issue in applying the risk-neutral pricing method to option pricing is to find a suitable risk-neutral pricing measure
The informative risk-neutral moments (RNMs) can be retrieved from a set of market-available options and utilized to correctly capture the features of the risk-neutral distribution (RND) for option pricing
We provide the general expression for extracting the RNMs and prove that the calculated
Summary
The key issue in applying the risk-neutral pricing method to option pricing is to find a suitable risk-neutral pricing measure (or risk-neutral distribution, RND). The resultant RND derived within the canonical valuation framework is a martingale measure and is reasonably regarded as the “best” RND for option pricing. This paper sets up an entropy valuation framework by incorporating the informative RNMs serving as constraints, nesting the sole martingale constraint into Stutzer’s canonical valuation, within which the “best” risk-neutral distribution (RND) is derived as the equivalent martingale measure for pricing European options. To deeply assess the efficacy of this RNM-based entropy valuation, the accuracy of the exacted RNMs and the risk-neutralities of resultant RND are verified, and the pricing performance is fully evaluated. This proposed entropy valuation has the following advantages.
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