Implied Volatility Surface: Construction Methodologies and Characteristics
The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to perform extrapolation outside the core region, choice of calibrating functional and selection of numerical optimization algorithms, volatility surface dynamics and asymptotics.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Martin Forde & Antoine Jacquier, 2009. "Small-Time Asymptotics For Implied Volatility Under The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 861-876.
- Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
- Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
- Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
- S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
- Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
- Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
Econometric Society, vol. 68(6), pages 1343-1376, November.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
- Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO.
- E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
- Matthias Fengler, 2010. "Option data and modeling BSM implied volatility," University of St. Gallen Department of Economics working paper series 2010 2010-32, Department of Economics, University of St. Gallen.
- Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
- Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
- Jan Obloj, 2007. "Fine-tune your smile: Correction to Hagan et al," Papers 0708.0998, arXiv.org, revised Mar 2008.
- Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
- Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
- Jose E. Figueroa-Lopez & Martin Forde, 2011. "The small-maturity smile for exponential Levy models," Papers 1105.3180, arXiv.org, revised Dec 2011.
- S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
- M. Benko & M. Fengler & W. Härdle & M. Kopa, 2007. "On extracting information implied in options," Computational Statistics, Springer, vol. 22(4), pages 543-553, December.
- Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
- Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
- Alexey Medvedev & Olivier Scaillet, "undated". "Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility," Swiss Finance Institute Research Paper Series 06-08, Swiss Finance Institute, revised Jan 2006.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Alexey Medvedev, 2004. "Implied Volatility at Expiration," Swiss Finance Institute Research Paper Series 08-04, Swiss Finance Institute, revised Jan 2008.
- Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
- A. Elices, 2007. "Models with time-dependent parameters using transform methods: application to Heston's model," Papers 0708.2020, arXiv.org, revised Oct 2008.
- Lindström, Erik & Ströjby, Jonas & Brodén, Mats & Wiktorsson, Magnus & Holst, Jan, 2008. "Sequential calibration of options," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2877-2891, February.
- Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
- Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
- Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
- Martin Forde & Antoine Jacquier, 2011. "Small-Time Asymptotics for an Uncorrelated Local-Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 517-535, April.
- Laurini, Márcio P., 2007. "Imposing No-Arbitrage Conditions In Implied Volatility Surfaces Using Constrained Smoothing Splines," Insper Working Papers wpe_89, Insper Working Paper, Insper Instituto de Ensino e Pesquisa. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1107.1834. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.