An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer’s call policies. Increasingly pessimistic values for the issuer’s substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.call notice period, call premium, convertible bond, delayed calls, equity-linked default, stochastic interest rates, volatility uncertainty

Interest Term Premiums and C-CAPM: A Test of a Parsimonious Model

This paper proposes a consumption-based model that accounts for term premiums of the nominal term structure of interest rates. The driving force behind the model is the looking at the ex ante term premium. Nominal term premiums depend on the volatility processes of real consumption and inflation. When calibrated to US data on interest rates, consumption and inflation, the model accounts for the C-CAPM expectations puzzle. Risk aversion coefficients around 6 are evidenced. The hypothesis of non-constant subjective discount rates is envisaged but successfully validated.C-CAPM, term structure of interest rates, term premium, risk aversion, subjective discount factor

Convertible Bonds: Risks and Optimal Strategies

Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasi˘cekâmodel is applied to incorporate interest rate risk into the firmâs value process which follows a geometric Brownian motion. Finally, we derive pricing bounds for convertible bonds in an uncertain volatility model, i.e. when the volatility of the firm value process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk