Valuation of embedded options in non-marketable callable bonds: a new numerical approach

Abstract

The issue of how to price options embedded in callable bonds has attracted a lot of interest over the years. The usual bond valuation methods rely on yield curves, risk premium, and other parameters to estimate interest rates used in discounted cash flow calculations. The option to retire the bond is, however, neglected in the standard pricing models, causing a systematic overvaluation of callable bonds. In the event of a decline in interest rates, investors are exposed to the risk of a lower return on investment than indicated by the yield to maturity. We propose a novel approach to valuing the risk that the issuer will use the right to buy back the bond at a specific call price. While prior models are focused on valuing marketable callable bonds, we deliver a unique approach to valuing bonds with an embedded European option (or a multiple option) that are traded solely through private transactions. These can typically be characterized by the lack of historical records on transaction prices. The modular character of calculation we propose allows us to take into account additional information, such as probable behaviour of the issuer, available opportunities for achieving alternative earnings or different estimates in terms of interest rate development.