Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility
发现债券市场并非完全覆盖固定收益衍生品，即互换利率对波动率风险组合的解释力有限，提出非跨期随机波动率概念，并给出三变量马尔可夫仿射系统满足该特征的条件。
ABSTRACT Most term structure models assume bond markets are complete, that is, that all fixed income derivatives can be perfectly replicated using solely bonds. How ever, we find that, in practice, swap rates have limited explanatory power for returns on at‐the‐money straddles—portfolios 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 USV models, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.