This page lists classical and recent references related to models of stochastic volatility, primarily for equities, but also FX and fixed income. There are naturally many overlaps with the other topics pages. The links are by no means exhaustive: please do not hesitate to email mailto:sircar@princeton.edu with any suggestions and additions.
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Classical References
J. Hull & A. White (1987): The pricing of options on assets with stochastic volatility, Journal of Finance 42(2), 281-300.
J. Wiggins (1987): Option values under stochastic volatility, Journal of Financial Economics 19(2), 351-372.
L. Scott (1987): Option pricing when the variance changes randomly: Theory, estimation and an application, Journal of Financial and Quantitative Analysis 22(4), 419-438.
Surveys
R. Frey (1996): Derivative Asset Analysis in Models with Level Dependent and Stochastic Volatility, CWI Quaterly 10, no 1 (special issue on the Mathematics of Finance) pages 1-34.
D. Hobson (1996): Stochastic Volatility, in Statistics in Finance, editors D. Hand and S. Jacka, Applications of Statistics Series, Arnold, London. 1998
E. Ghysels, A. Harvey, E. Renault (1996): Stochastic Volatility, in Statistical Methods in Finance (Handbook of Statistics, vol. 14), G.Maddala and C. Rao (eds.), pages 119-191.
O.E. Barndorff-Nielsen,
Books
A. Lewis (2000): Option Valuation under Stochastic Volatility, Finance Press.
J.-P. Fouque, G. Papanicolaou
and K.R. Sircar (2000): Derivatives
in Financial Markets with Stochastic Volatility,
Recent Papers
Jumps
G. Bakshi, C. Cao, Z. Chen (1997): Empirical Performance of Alternative Option Pricing Models, Journal of Finance 52, No. 5, 1997, 2003-2049.
D. Duffie, J. Pan, K. Singleton (2000): Transform Analysis and Asset Pricing for Affine Jump-Diffusions, Econometrica, Volume 68, pages 1343--1376.
Peter Carr, He'lyette Geman, Dilip B. Madan and Marc Yor (2003): Stochastic Volatility for Levy Processes, Mathematical Finance, to appear.
SABR Model
P. Hagan, D. Kumar, A. Lesniewski and D. Woodward: Managing Smile Risk
Empirical Analysis of Returns/Statistical Methods
Y. Ait-Sahalia (2004): Disentangling Diffusion from Jumps, Journal of Financial Economics, to appear.
O.E. Barndorff-Nielsen, N. Shephard (2004): Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics, Econometrica, Volume 72 Issue 3 Page 885 - 925.
T. Andersen, T. Bollerslev, F. Diebold, P. Labys (2003): Modeling and Forecasting Realized Volatility, Econometrica Volume 71, 529-626.
Empirical Analysis of Implied Volatilities
J.-P. Fouque, G. Papanicolaou, R. Sircar, K. Solna (2004): Maturity Cycles in Implied Volatility, Finance and Stochastics, to appear.