Benchmark-neutral pricing

Eckhard Platen

Quantitative Finance, 2025, vol. 25, issue 12, 1907-1919

Abstract: The paper proposes benchmark-neutral pricing and hedging for long-term contingent claims. It employs the growth optimal portfolio of the stocks as numéraire and the new benchmark-neutral pricing measure for pricing. For the assumed ‘natural’ dynamics of a well-diversified stock portfolio, which are those of the continuous limit of a branching process of diversified wealth in some activity time, this pricing measure turns out to be an equivalent probability measure. This is not the case for the putative risk-neutral pricing measure. Benchmark-neutral pricing identifies the minimal possible prices of contingent claims. Risk-neutral prices of long-term contracts can be significantly more expensive than necessary. The extremely accurate hedge of a long-term zero-coupon bond illustrates the proposed pricing and hedging method.

Date: 2025
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DOI: 10.1080/14697688.2025.2577115

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