Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility

Abstract

Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on at-the-money straddlesportfolios mainly exposed to volatility risk. We term this empirical feature "unspanned stochastic volatility" (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USVmodels, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.

Bond risk premia and realized jump risk

“…In fact, they are small -ranging from 4 to 20%. This has previously been shown for realized volatility (Andersen and Benzoni, 2008) and for implied volatility (Collin-Dufresne and Goldstein, 2002). But it is true for our jump risk measures too.…”

Rate fears gauges and the dynamics of fixed income and equity volatilities

“…We, thus, considerably depart from standard literature, which relied on parametric assumptions on interest rate volatility (e.g., Collin-Dufresne and Goldstein, 2002;Mele, 2003;Joslin, 2010;and references therein). A natural avenue for future research is the modeling of the stylized facts uncovered in the paper.…”

Pricing and hedging interest rate options: Evidence from cap–floor markets

“…However, none of these models is able to price swaptions accurately, leading them to conclude that there may be need for non-affine models to price interest rate derivatives. In fact, Collin-Dufresne and Goldstein (2002) argue that there is a missing stochastic volatility factor that affects the prices of interest rate options, but does not affect the underlying LIBOR or swap rates. They propose models with explicit factors driving volatility, and suggest that cap prices may not be explained well by term structure models that only include yield curve factors.…”