Pricing collateralized derivatives with an arbitrary numeraire

Joanne Kennedy

Mathematical Finance, 2020, vol. 30, issue 2, 464-500

Abstract: 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.

Date: 2020
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