Since the 2008 crisis collateralized derivatives have become commonplace in the market. There have been many papers in recent years on pricing collateralized derivatives but the topic has been surrounded by confusion with debate focusing on whether or not a risk‐free rate needs to be assumed. In addition, as pointed out by Bielecki and Rutkowski, several authors do not pay enough attention to the pricing measure they are working in when setting up their models. The contribution of this paper is to show the pricing formula for a collateralized derivative can be derived under the usual assumptions of an arbitrage‐free economy starting from any equivalent martingale measure and associated numeraire.

中文翻译：

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用任意数值对抵押衍生品定价

自2008年危机以来，抵押衍生品已在市场上变得司空见惯。近年来，有很多关于抵押衍生品定价的论文，但是这个话题一直困扰着围绕是否需要假设无风险利率的辩论。此外，正如Bielecki和Rutkowski所指出的那样，几位作者在建立模型时并未对他们正在采用的定价方法给予足够的重视。本文的目的是表明，在无套利经济的通常假设下，抵押衍生品的定价公式可以从任何等效的measure值和相关的计价方法开始推导。