Valuation of Callable/Putable Corporate Bonds in a One-Factor LogNormal Interest-Rate Model

Abstract

Whereas the callable-bond market used to emphasize primarily public debt—Government Agencies, and both investment grade and non-investment corporate debt—that has changed dramatically over the past twenty years, in part due to the low prevailing rates of interest as well as some systematic changes in the Agency sector. While some Agency and investment grade corporate bonds are still extant, there are more numerous callable bonds of lower ratings categories. In delivering a theoretically-sound practical model, one that does not call for computation or use of an “option-adjusted spread” (OAS), this article seeks to use a one-factor LogNormal interest-rate model to calibrate the implied-vols of callable and putable bonds in the U.S. bond market, and to relate those implied volatilities to measures of time to call, time from call to maturity, moneyness and the credit-yield spread.

TOPICS: Fixed income and structured finance, derivatives, options, quantitative methods, statistical methods

Key Findings

• ▪ Valuation of callable and putable bonds in a theoretically-sound practical model that does not use “option-adjusted spreads” (OAS).

• ▪ A one-factor LogNormal interest-rate model is used to calibrate implied-vols of callable and putable bonds in the US corporate and agency bond markets.

• ▪ Volatility calibration uses observed bonds’ market prices to elicit dependence of priced volatility on time to first call, time from call to maturity, moneyness and the credit-yield spread.