509
Views
10
CrossRef citations to date
0
Altmetric
Research Article

Detecting and Repairing Arbitrage in Traded Option Prices

ORCID Icon, ORCID Icon & ORCID Icon
Pages 345-373 | Received 21 Aug 2020, Accepted 27 Oct 2020, Published online: 08 Feb 2021

References

  • Aït-Sahalia, Y., and J. Duarte. 2003. “Nonparametric Option Pricing under Shape Restrictions.” Journal of Econometrics 116 (1–2): 9–47. doi:10.1016/S0304-4076(03)00102-7.
  • Blacque-Florentin, P. M., and B. Missaoui. 2016. “Nonparametric and Arbitrage-free Construction of Call Surfaces Using l1-recovery.” Arxiv:1506.06997.
  • Boyd, S., and L. Vandenberghe. 2004. Convex Optimization. New York, NY, USA: Cambridge University Press.
  • Breeden, D. T., and R. H. Litzenberger. 1978. “Prices of State-contingent Claims Implicit in Option Prices.” The Journal of Business 51 (4): 621–651. doi:10.1086/296025.
  • Candes, E., M. Rudelson, T. Tao, and R. Vershynin. 2005. “Error Correction via Linear Programming.” In 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05), 668–681. Pittsburgh, PA.
  • Carr, P., and D. B. Madan. 2005. “A Note on Sufficient Conditions for No Arbitrage.” Finance Research Letters 2 (3): 125–130. doi:10.1016/j.frl.2005.04.005.
  • Carr, P., H. Geman, D. Madan, and M. Yor. 2003. “Stochastic Volatility for Lévy Processes.” Mathematical Finance 13 (3): 345–382. doi:10.1111/1467-9965.00020.
  • Chataigner, M., S. Crépey, and M. Dixon. 2020. “Deep Local Volatility.” Arxiv Preprint Arxiv:2007.10462.
  • Cousot, L. 2007. “Conditions on Option Prices for Absence of Arbitrage and Exact Calibration.” Journal of Banking & Finance 31 (11): 3377–3397. doi:10.1016/j.jbankfin.2007.04.006.
  • Davis, M. H. A., and D. G. Hobson. 2007. “The Range of Traded Option Prices.” Mathematical Finance 17 (1): 1–14. doi:10.1111/j.1467-9965.2007.00291.x.
  • Delbaen, F., and W. Schachermayer. 1994. “A General Version of the Fundamental Theorem of Asset Pricing.” Mathematische Annalen 300 (1): 463–520. doi:10.1007/BF01450498.
  • Derman, E., and I. Kani. 1994. “Riding on a Smile.” Risk 7: 32–39.
  • Donoho, D. L., and M. Elad. 2003. “Optimally Sparse Representation in General (Nonorthogonal) Dictionaries via L1 Minimization.” Proceedings of the National Academy of Sciences 100 (5): 2197–2202. doi:10.1073/pnas.0437847100.
  • Dupire, B. 1994. “Pricing with a Smile.” Risk Magazine 7: 18–20.
  • Fengler, M. 2009. “Arbitrage-free Smoothing of the Implied Volatility Surface.” Quantitative Finance 9: 417–428. doi:10.1080/14697680802595585.
  • Fengler, M. 2012. “Option Data and Modeling BSM Implied Volatility.” In Handbook of Computational Finance, edited by J.-C. Duan, W. K. Härdle, and J. E. Gentle, 117–142. Berlin, Heidelberg: Springer.
  • Fengler, M. R., and L.-Y. Hin. 2015. “Semi-nonparametric Estimation of the Call-option Price Surface under Strike and Time-to-expiry No-arbitrage Constraints.” Journal of Econometrics 184 (2): 242–261. doi:10.1016/j.jeconom.2014.09.003.
  • Gatheral, J., and A. Jacquier. 2014. “Arbitrage-free SVI Volatility Surfaces.” Quantitative Finance 14 (1): 59–71. doi:10.1080/14697688.2013.819986.
  • Gerhold, S., and I. C. Gülüm. 2020. “Consistency of Option Prices under Bid–Ask Spreads.” Mathematical Finance 30 (2): 377–402. doi:10.1111/mafi.12230.
  • Gribonval, R., and M. Nielsen. 2003. “Sparse Representations in Unions of Bases.” IEEE Transactions on Information Theory 49 (12): 3320–3325. doi:10.1109/TIT.2003.820031.
  • Harrison, J. M., and D. Kreps. 1979. “Martingales and Arbitrage in Multiperiod Securities Markets.” Journal of Economic Theory 20 (3): 381–408. doi:10.1016/0022-0531(79)90043-7.
  • Heston, S. L. 1993. “A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies 6: 327–343. doi:10.1093/rfs/6.2.327.
  • Huber, P. J., and E. M. Ronchetti. 2009. Robust Statistics. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc.
  • Ivanovas, A. 2015. “Option Data, Missing Tails, and the Intraday Variation of Implied Moments.” PhD thesis, University of St. Gallen.
  • Kahale, N. 2004. “An Arbitrage-free Interpolation of Volatilities.” Risk Magazine 17: 102–106.
  • Kellerer, H. G. 1972. “Markov-Komposition und eine Anwendung auf Martingale.” Mathematische Annalen 198: 99–122. doi:10.1007/BF01432281.
  • Kreps, D. 1981. “Arbitrage and Equilibrium in Economies with Infinitely Many Commodities.” Journal of Mathematical Economics 8 (1): 15–35. doi:10.1016/0304-4068(81)90010-0.
  • Le Floc’h, F., C. W. Oosterlee. 2019. “Model-free Stochastic Collocation for an Arbitrage-free Implied Volatility, Part Ii.” Risks 7 (1): 1–21. doi:10.3390/risks7010030.
  • Lim, H. 2020. “Improved Methods for Implied Volatility Surface and Implied Distributions.” SSRN Preprint 3561100.
  • Martin, L. V., S. Andersen, and J. Dahl. 2000. “Cvxopt: A Python Package for Convex Optimization.” Version 1.2.5; available at cvxopt.org.
  • Meier, P. 2015. “Essays on Pricing Kernel Estimation, Option Data Filtering and Risk-neutral Density Tail Estimation.” PhD thesis, University of St. Gallen.
  • Natarajan, B. K. 1995. “Sparse Approximate Solutions to Linear Systems.” SIAM Journal on Computing 24 (2): 227–234. doi:10.1137/S0097539792240406.
  • Ruf, J., and W. Wang. 2019. “Neural Networks for Option Pricing and Hedging: A Literature Review.” SSRN Preprint 3486363.
  • Shaked, M., and J. Shanthikumar. 2007. Stochastic Orders. Springer New York: Springer Series in Statistics.
  • Stoikov, S. 2018. “The Micro-price: A High-frequency Estimator of Future Prices.” Quantitative Finance 18: 1–8. doi:10.1080/14697688.2018.1489139.
  • Wang, Y., H. Yin, and L. Qi. 2004. “No-arbitrage Interpolation of the Option Price Function and Its Reformulation.” Journal of Optimization Theory and Applications 120 (3): 627–649. doi:10.1023/B:JOTA.0000025713.44548.71.
  • Wystup, U. 2017. FX Options and Structured Products. John Wiley & Sons, Ltd.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.