Arbitrage problems with reflected geometric Brownian motion

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE Finance and Stochastics Pub Date : 2023-12-20 DOI:10.1007/s00780-023-00525-x

Dean Buckner, Kevin Dowd, Hardy Hulley

引用次数: 0

Abstract

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

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反映几何布朗运动的套利问题

与几位作者的说法相反，在金融市场模型中，风险证券的价格遵循反射几何布朗运动，并不是无套利的。事实上，这种模型甚至违反了文献中认为的最弱的无套利条件。因此，它们不允许采用数字投资组合或等效的风险中性概率度量，这使得它们不适合或有索赔估值。不足为奇的是，已公布的此类模型的期权定价公式违反了经典的无套利约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.

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