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.

Callable Bond's Value Analysis Using Binomial Interest Rate Tree Considering Early Redemption and Default Risks

“…As the centre of economic theories, models, and systems, interest rate volatility plays a major role in the development of valuation method of bond and its derivatives (Markellos & Psychoyios, 2018). Skalický et al (2022) note that, in the event of declining interest rates, the risk of a lower return on investment might be posed to investors. However, callable bond investors are exposed to one more risk, that is early redemption risk.…”

“…Díaz & Tolentino (2020) examined interest rate risk in bonds with embedded options, comparing both the Ho & Lee (1986) model which follows the binomial distribution and utilizes Wiener process that can still produce negative interest rates and Black et al (1990) model that follows the lognormal distribution resulting in nonnegative interest rates. Skalický et al (2022) proposed an approach to valuing bonds with an embedded European option based on models describing the evolution of interest rates (Cox et al, 1985;Marsh & Rosenfeld, 1983;Vasicek, 1977). By extending the Ho-Lee model, Kim et al (2017) improved the model to produce a more realistic and flexible model.…”

“…Default risk occurs when the bond issuer fails to meet the payment of interest and repayment of the amount borrowed on time (Baker et al, 2019;Fabozzi & Fabozzi, 2021). Skalický et al (2022) summarized how callable bonds and default risk are connected. First, callable bonds are predominantly issued by firms facing higher default risk since they suffer from the lack of positive NPV projects (Elsaify & Roussanov, 2016).…”