都有哪些估計隱含波動率曲面 (Implied Volatility Surface) 的模型？

波動率

剛好最近在看IVS相關論文，總結如下：

1. (Local) Stochastic Volatility Model

1.1. Heston Model
J. Gatheral. The Volatility Surface: A practitioner』s guide. Wiley Finance, 2006.
E. Benhamou, E. Gobet, and M. Miri. Time dependent Heston model. SIAM Journal of Financial
Mathematics, 1:289–325, 2010.

1.2. SABR Model
P. Hagan, D. Kumar, A. Lesniewski, and D. Woodward. Managing smile risk. Wilmott, 1(8):84–108,2002.
P. Gauthier and P.-Y. H. Rivaille. Fitting the smile: Smart parameters for SABR and Heston.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1496982, 2009.
P. Henry-Labordere. Geometry and Modeling in Finance: Advanced Methods in Option Pricing.
Chapman and Hall, 2008.

1.3. Local Stochastic Model
J. Maruhn. Calibration of stochastic and local stochastic volatility models. In Global Derivatives
Trading Risk Management, Paris, April 11-15, 2011.

1.4. Brigo-Mercurio Lognormal-mixture local volatility model
Brigo D, Mercurio F. Lognormal-mixture dynamics and calibration to market volatility smiles[J]. International Journal of Theoretical and Applied Finance, 2002, 5(04): 427-446.

2. Levy process
2.1. Implied Levy Volatility
J. M. Corcuera, F. Guillaume, P. Leoni, and W. Schoutens. Implied Lévy volatility. Quantitative
Finance, 9(4):383–393, 2009.

3. Dynamics of implied volatility
3.1. Carr and Wu approach
P. Carr and L. Wu. A new simple approach for constructing implied volatility surfaces. http://
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1701685, 2010.

4. Parametric representations
4.1. Polynomial parametrization
B. Dumas, J. Fleming, and R.E. Whaley. Implied volatility functions: Empirical tests. The Journal
of Finance, (53), 1998.
S. Borovkova and F. J. Permana. Implied volatility in oil markets. Computational Statistics and
Data Analysis, 53:2022–2039, April 2009.

4.2. Stochastic volatility inspired parametrization
J Gatheral. A parsimonious arbitrage-free implied volatility parameterization with application to
the valuation of volatility derivatives. http://www.math.nyu.edu/fellows_fin_math/gatheral/
madrid2004.pdf, 2004.
J. Gatheral. The Volatility Surface: A practitioner』s guide. Wiley Finance, 2006.

4.3. Entropy based parametrization
M. Avellaneda, C. Friedman, R. Holmes, and D. Samperi. Calibrating volatility surfaces via relativeentropy minimization. Appl. Math. Finance, 4(1):37–64, 1997.
D.C. Brody, I.R.C. Buckley, and I.C. Constantinou. Option price calibration from Rényi entropy.
Physics Letters A, 366:298–307, July 2007.
P. W. Buchen and M. Kelly. The maximum entropy distribution of an asset inferred from option
prices. Journal of Financial and Quantitative Analysis, 31(01):143–159, March 1996.

4.4. weighted lognormal distribution
D.A. Bloch. A practical guide to implied and local volatility. http://papers.ssrn.com/sol3/
papers.cfm?abstract_id=1538808, 2010.
D.A. Bloch and C.A. Coello Coello. Smiling at evolution. http://papers.ssrn.com/sol3/papers.
cfm?abstract_id=1627645, 2010.

5. Nonparametric representations
5.1. spline
G.Wolberg and I. Alfy. An energy-minimization framework for monotonic cubic spline interpolation. Journal of Computational and Applied Mathematics, 143:145–188, 2002.

5.2. implicit finite difference discretization of Dupire forward PDE
J Andreasen and B. Huge. Volatility interpolation. http://papers.ssrn.com/sol3/papers.cfm?
abstract_id=1694972, 2010.
J Andreasen and B Huge. Volatility interpolation. Risk magazine, March, 2011.
B Huge. Volatility interpolation. In Quant Congress Conference, 2010.