Pricing options embedded in debentures with credit risk

Abstract

In this article, we develop a strategy to simultaneously extract a yield curve and price call options embedded in debentures subject to credit risk. The implementation is based on a combination of two methods: term structure estimation adopting the Nelson-Siegel model sequentially followed by the use of the spread-curve (term structure of debentures minus local inter-bank risk-free rate) to calibrate a trinomial tree for short-term interest rates making use of the Hull and White model (1993). The proposed methodology allows us to price embedded options making debentures with and without embedded options comparable on a common basis. As a consequence, since a large number of the existing Brazilian debentures contain embedded options, our methodology increases the number of debentures available to estimate a term structure for Brazilian local fixed income bonds. We illustrate the method by pricing a call option for a debenture issued by the company “Telefonica Brasil”.