Can a Machine Correct Option Pricing Models?

CBS−1 f(.) z0=xi,t d0=2 L≥2 Et[Vt+h]=v¯̂+e−κ̂h/252(V̂t−v¯̂) V̂t ξ=(v¯,κ,σv,ρ) References

• Ackerer, D., Tagasovska, N., Vatter, T. (2020), “Deep Smoothing of the Implied Volatility Surface,” Advances in Neural Information Processing Systems, 33, 11552–11563.
   Google Scholar
• Amilon, H. (2003), “A Neural Network Versus Black–Scholes: A Comparison of Pricing and Hedging Performances,” Journal of Forecasting, 22, 317–335. DOI: 10.1002/for.867.
   Web of Science ®Google Scholar
• Ait-Sahalia, Y., and Lo, A. W. (1998),“Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,” The Journal of Finance, 53, 499–547. DOI: 10.1111/0022-1082.215228.
   Web of Science ®Google Scholar
• Ait-Sahalia, Y., and Duarte, J. (2003), “Nonparametric Option Pricing Under Shape Restrictions,” Journal of Econometrics, 116, 9–47. DOI: 10.1016/S0304-4076(03)00102-7.
   Web of Science ®Google Scholar
• Ait-Sahalia, Y., Li, C., and Li, C. X. (2021), “Implied Stochastic Volatility Models,” The Review of Financial Studies, 34, 394–450. DOI: 10.1093/rfs/hhaa041.
   Web of Science ®Google Scholar
• Andersen, T. G., Fusari, N., and Todorov, V. (2015), “The Risk Premia Embedded in Index Options,” Journal of Financial Economics, 117, 558–584. DOI: 10.1016/j.jfineco.2015.06.005.
   Web of Science ®Google Scholar
• Aruoba, S. B., Diebold, F. X., and Scotti, C. (2009), “Real-Time Measurement of Business Conditions,” Journal of Business and Economic Statistics, 27, 417–427. DOI: 10.1198/jbes.2009.07205.
   Web of Science ®Google Scholar
• Baker, S. R., Bloom, N., and Davis, S. J. (2016), “Measuring Economic Policy Uncertainty,” The Quarterly Journal of Economics, 131, 1593–1636. DOI: 10.1093/qje/qjw024.
   Web of Science ®Google Scholar
• Bakshi, G., Cao, C., and Chen, Z. (1997), “Empirical Performance of Alternative Option Pricing Models,” The Journal of Finance, 52, 2003–2049. DOI: 10.1111/j.1540-6261.1997.tb02749.x.
   Web of Science ®Google Scholar
• Bandi, F. M., Fusari, N., and Renò, R. (2021), “Structural Stochastic Volatility,” Unpublished working paper.
   Google Scholar
• Bates, D. (2000), “Post-’87 Crash Fears in the S&P 500 Futures Option Market,” Journal of Econometrics, 94, 181–238.
   Web of Science ®Google Scholar
• Bauer, B., and Kohler, M. (2019), “On Deep Learning as a Remedy for the Curse of Dimensionality in Nonparametric Regression,” Annals of Statistics, 47, 2261–2285.
   Web of Science ®Google Scholar
• Black, F., and Scholes, M. (1973), “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81, 637–654. DOI: 10.1086/260062.
   Web of Science ®Google Scholar
• Bollerslev, T., Todorov, V., and Xu, L. (2015), “Tail Risk Premia and Return Predictability,” Journal of Financial Economics, 118, 113–134. DOI: 10.1016/j.jfineco.2015.02.010.
   Web of Science ®Google Scholar
• Breeden, D., and Litzenberger, R. H. (1978), “Prices of State-Contingent Claims Implicit in Option Prices,” Journal of Business, 51, 621–651. DOI: 10.1086/296025.
   Web of Science ®Google Scholar
• Buhler, H., Gonon, L., Teichmann, J., and Wood, B. (2019), “Deep Hedging,” Quantitative Finance, 19, 1271–1291. DOI: 10.1080/14697688.2019.1571683.
   Web of Science ®Google Scholar
• Carr, P., and Wu, L. (2016), “Analyzing Volatility Risk and Risk Premium in Option Contracts: A New Theory,” Journal of Financial Economics, 120, 1–20. DOI: 10.1016/j.jfineco.2016.01.004.
   Web of Science ®Google Scholar
• Cybenko, G. (1989), “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals and Systems, 2, 303–314. DOI: 10.1007/BF02551274.
   Google Scholar
• Duffie, D., Pan, J., and Singleton, K. (2000), “Transform Analysis and Asset Pricing for Affine Jump-Diffusions,” Econometrica, 68, 1343–137. DOI: 10.1111/1468-0262.00164.
   Web of Science ®Google Scholar
• Dugas, C., Bengio, Y., Belisle, F., Nadeau, C., and Garcia, R. (2009), “Incorporating Functional Knowledge in Neural Networks,” Journal of Machine Learning Research, 10, 1239–1262.
   Web of Science ®Google Scholar
• Dumas, B., Fleming, J., Whaley, R. E. (1998), “Implied Volatility Functions: Empirical Tests,” The Journal of Finance, 53, 2059–2106. DOI: 10.1111/0022-1082.00083.
   Web of Science ®Google Scholar
• Dupire, B. (1994), “Pricing with a Smile,” Risk, 7, 18–20.
   Google Scholar
• Fan, J., Ma, C., and Zhong, Y. (2021), “A Selective Overview of Deep Learning,” Statistical Science, 36, 264–290. DOI: 10.1214/20-sts783.
   PubMed Web of Science ®Google Scholar
• Fan, J., and Mancini, L. (2009), “Option Pricing with Model-Guided Nonparametric Methods,” Journal of the American Statistical Association, 104, 1351–1372. DOI: 10.1198/jasa.2009.ap08171.
   Web of Science ®Google Scholar
• Fan, J., Wu, Y., and Feng, Y. (2009), “Local Quasi-Likelihood with a Parametric Guide,” Annals of Statistics, 37, 4153–4183.
   PubMed Web of Science ®Google Scholar
• Fan, Y., and Ullah, A. (1999), “Asymptotic Normality of a Combined Regression Estimator,” Journal of Multivariate Analysis, 71, 191–240. DOI: 10.1006/jmva.1999.1838.
   Web of Science ®Google Scholar
• Fang, F., and Oosterlee, C. W. (2009), “A Novel Pricing Method for European Options based on Fourier-Cosine Series Expansions,” SIAM Journal on Scientific Computing, 31, 826–848. DOI: 10.1137/080718061.
   Web of Science ®Google Scholar
• Garcia, R., and Gençay, R. (2000), “Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint,” Journal of Econometrics, 94, 93–115. DOI: 10.1016/S0304-4076(99)00018-4.
   Web of Science ®Google Scholar
• Gatheral, J., and Jacquier, A. (2014), “Arbitrage-Free SVI Volatility Surfaces,” Quantitative Finance, 14, 59–71. DOI: 10.1080/14697688.2013.819986.
   Web of Science ®Google Scholar
• Glad, I. K. (1998), “Parametrically Guided Non-parametric Regression,” Scandinavian Journal of Statistics, 25, 649–668. DOI: 10.1111/1467-9469.00127.
   Web of Science ®Google Scholar
• Gonçalves, S., and Guidolin, M. (2006), “Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface,” Journal of Business, 79, 1591–1635.
   Google Scholar
• Gu, S., Kelly, B., and Xiu, D. (2020), “Empirical Asset Pricing via Machine Learning,” The Review of Financial Studies, 33, 2223–2273. DOI: 10.1093/rfs/hhaa009.
   Web of Science ®Google Scholar
• Heston, S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” The Review of Financial Studies, 6, 327–343. DOI: 10.1093/rfs/6.2.327.
   Web of Science ®Google Scholar
• Hornik, K., Stinchcombe, M., and White, H. (1989), “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks, 2, 359–366. DOI: 10.1016/0893-6080(89)90020-8.
   Web of Science ®Google Scholar
• Hutchinson, J. M., Lo, A. W., and Poggio, T. (1994), “A Nonparametric Approach to the Pricing and Hedging of Derivative Securities via Learning Networks,” The Journal of Finance, 49, 851–889. DOI: 10.1111/j.1540-6261.1994.tb00081.x.
   Web of Science ®Google Scholar
• Jackwerth, J. C., and Rubinstein, M. (1996), “Recovering Probability Distributions from Option Prices,” The Journal of Finance, 51, 1611–1631. DOI: 10.1111/j.1540-6261.1996.tb05219.x.
   Web of Science ®Google Scholar
• Liu, S., Oosterlee, C. W., and Bohte, S. (2019), “Pricing Options and Computing Implied Volatilities using Neural Networks,” Risks, 7, 1–22. DOI: 10.3390/risks7010016.
   Web of Science ®Google Scholar
• Masters, T. (1993), “Practical Neural Network Recipes in C++,” New York: Academic Press.
   Google Scholar
• Medvedev, A., and Scaillet, O. (2007), “Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility,” The Review of Financial Studies, 20, 427–459. DOI: 10.1093/rfs/hhl013.
   Web of Science ®Google Scholar
• Mhaskar, H., Liao, Q., and Poggio, T. (2016), “Learning Functions: When is Deep Better Shallow,” Center for Brains, Minds and Machines (CBMM) Memo 45.
   Google Scholar
• Moller, M. F. (1993), “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, 6, 525–533.
   Web of Science ®Google Scholar
• Oh, D. H. and Patton, A. J. (2021), “Better the Devil You Know: Improved Forecasts from Imperfect Models,” Unpublished working paper.
   Google Scholar
• Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B., and Liao, Q. (2017), “Why and When can Deep-but not Shallow-Networks Avoid the Curse of Dimensionality: A Review,” International Journal of Automation and Computing, 14, 503–519. DOI: 10.1007/s11633-017-1054-2.
   Web of Science ®Google Scholar
• Rolnick, D., and Tegmark, M. (2018), “The Power of Deeper Networks for Expressing Natural Functions,” in International Conference on Learning Representations.
   Google Scholar
• Ross, S. A. (1976), “Options and Efficiency,” The Quarterly Journal of Economics, 90, 75–89. DOI: 10.2307/1886087.
   Web of Science ®Google Scholar
• Rubinstein, M. (1994), “Implied Binomial Trees,” The Journal of Finance, 49, 771–818. DOI: 10.1111/j.1540-6261.1994.tb00079.x.
   Web of Science ®Google Scholar
• Ruf, J., and Wang, W. (2021), “Hedging with Linear Regressions and Neural Networks,” Journal of Business and Economic Statistics (forthcoming). DOI: 10.1080/07350015.2021.1931241.
   PubMed Web of Science ®Google Scholar
• Stutzer, M. (1996), “A Simple Nonparametric Approach to Derivative Security Valuation,” The Journal of Finance, 51, 1633–1652. DOI: 10.1111/j.1540-6261.1996.tb05220.x.
   Web of Science ®Google Scholar
• Todorov, V. (2019), “Nonparametric Spot Volatility from Options,” Annals of Applied Probability, 29, 3590–3636.
   Web of Science ®Google Scholar