Unspanned stochastic volatility and fixed income derivatives pricing

Jaime Casassus, Pierre Collin-Dufresne, Bob Goldstein

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We propose a parsimonious 'unspanned stochastic volatility' model of the term structure and study its implications for fixed-income option prices. The drift and quadratic variation of the short rate are affine in three state variables (the short rate, its long-term mean and variance) which follow a joint Markov (vector) process. Yet, bond prices are exponential affine functions of only two state variables, independent of the current interest rate volatility level. Because this result holds for an arbitrary volatility process, such a process can be calibrated to match fixed income derivative prices. Furthermore, this model can be 'extended' (by relaxing the time-homogeneity) to fit any arbitrary term structure. In its 'HJM' form, this model nests the analogous stochastic equity volatility model of Heston (1993) [Heston, S.L., 1993. A closed form solution for options with stochastic volatility. Review of Financial Studies 6, 327-343]. In particular, if the volatility process is specified to be affine, closed-form solutions for interest rate options obtain. We propose an efficient algorithm to compute these prices. An application using data on caps and floors shows that the model can capture very well the implied Black spot volatility surface, while simultaneously fitting the observed term structure.

Original languageEnglish (US)
Pages (from-to)2723-2749
Number of pages27
JournalJournal of Banking and Finance
Issue number11
StatePublished - Nov 2005
Externally publishedYes


  • HJM
  • Stochastic volatility
  • Term structure


Dive into the research topics of 'Unspanned stochastic volatility and fixed income derivatives pricing'. Together they form a unique fingerprint.

Cite this