TY - JOUR

T1 - Unspanned stochastic volatility and fixed income derivatives pricing

AU - Casassus, Jaime

AU - Collin-Dufresne, Pierre

AU - Goldstein, Bob

PY - 2005/11

Y1 - 2005/11

N2 - 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.

AB - 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.

KW - HJM

KW - Stochastic volatility

KW - Term structure

UR - http://www.scopus.com/inward/record.url?scp=25144435359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144435359&partnerID=8YFLogxK

U2 - 10.1016/j.jbankfin.2005.02.007

DO - 10.1016/j.jbankfin.2005.02.007

M3 - Article

AN - SCOPUS:25144435359

SN - 0378-4266

VL - 29

SP - 2723

EP - 2749

JO - Journal of Banking and Finance

JF - Journal of Banking and Finance

IS - 11

ER -