Abstract In this paper, I show the validity of and the relationship between two previously unrelated claims in monetary theory. The first claim, made by Earl Thompson, is that privately-issued bank notes pay a positive rate of return in a competitive equilibrium. The second claim, made by Fischer Black, is that it is possible to have a gold standard in which the gold reserves of the central bank are near zero. I show that both of these claims are correct under the assumption of complete markets and perfect commitment. The link between these claims is the Black-Scholes equation applied to convertible bank notes. In commodity-based monetary systems, bank notes are perpetual American options. I extend the model to consider the implications of a lack of commitment on the part of the bank and incomplete markets. I show that both arguments break down when banks lack commitment to redemption or markets are incomplete. I conclude with implications for macroeconomic theory.

中文翻译：

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金融理论中竞争性发行的可转换银行票据：伯爵汤普森会见菲舍尔布莱克

摘要 在本文中，我展示了货币理论中两个先前不相关的主张的有效性和关系。Earl Thompson 提出的第一个主张是，私人发行的钞票在竞争均衡中支付正回报率。Fischer Black 提出的第二个主张是，有可能建立一个金本位制，其中中央银行的黄金储备接近于零。我表明，在完全市场和完美承诺的假设下，这两种说法都是正确的。这些主张之间的联系是应用于可兑换钞票的布莱克-斯科尔斯方程。在以商品为基础的货币体系中，纸币是永久的美式期权。我扩展了模型以考虑银行缺乏承诺和不完整市场的影响。我表明，当银行缺乏对赎回的承诺或市场不完整时，这两种论点都会失效。最后，我总结了对宏观经济理论的影响。