I conduct a simulation study to address concerns raised in the empirical literature on unspanned stochastic volatility (USV, i.e., interest-rate-volatility risk that cannot be hedged with bonds or swaps). Regressions have been the popular method of identifying and measuring USV, and have led to a consensus that is in favour of USV models. Despite plausible challenges to this approach, my simulations show that regressions are able to correctly identify the presence and absence of USV. This relies on a number of methodological considerations which are inconsistent in the literature. Regression results from empirical data, from several modern interest-rate markets, resemble results from data simulated from USV models. I then assess the economic significance of USV. By comparing hedged and unhedged returns of market interest-rate options, I develop quantitative guidelines around how unspanned volatility risk compares to interest-rate risk.

Interest-rate benchmark reform has revived short-rate modelling. One reason is that short-rate models provide a consistent framework in which different benchmarks, and contracts linked to them, can be compared. Another reason is that new benchmarks can be directly dependent on very short-term rates; the key example is a backward-looking compounding of overnight rates, a prominent alternative to forward-looking Libor. Indeed, under Libor, one can often safely ignore aspects of short-rate behaviour, especially jumps. At least partially for this reason, jumps are inadequately treated in the interest-rate literature, particularly expected jumps (jumps with known timing). We estimate a model with expected and unexpected jumps, which involves separating their effect on term rates. We then price forward- and backward-looking caplets, quantifying the spread exhibited by the latter over the former. Expected jumps lead to significantly time-inhomogeneous option behaviour, particularly for short-term options linked to a backward-looking benchmark.