Abstract
We present a new semi-parametric model for the prediction of implied volatility surfaces that can be estimated using machine learning algorithms. Given a reasonable starting model, a boosting algorithm based on regression trees sequentially minimizes generalized residuals computed as differences between observed and estimated implied volatilities. To overcome the poor predictive power of existing models, we include a grid in the region of interest, and implement a cross-validation strategy to find an optimal stopping value for the boosting procedure. Back testing the out-of-sample performance on a large data set of implied volatilities from S&P 500 options, we provide empirical evidence of the strong predictive power of our model.
Similar content being viewed by others
References
Ait-Sahalia, Y., Lo, A.: Nonparametric estimation of state-price densities implicit in financial asset prices. J. Financ. 53(2), 499–547 (1998)
Audrino, F., Bühlmann, P.: Volatility estimation with functional gradient descent for very high-dimensional financial time series. J. Comput. Financ. 6(3), 1–26 (2003)
Audrino, F., Trojani, F.: Accurate short-term yield curve forecasting using functional gradient descent. J. Financ. Econom. 5(4), 591–623 (2007)
Audrino, F., Barone-Adesi, G., Mira, A.: The stability of factor models of interest rates. J. Financ. Econom. 3(3), 422–441 (2005)
Barone-Adesi, G.B.F., Giannopoulos, K.: Don’t look back. Risk 11, 100–104 (1998)
Barone-Adesi, G.G.K., Vosper, L.: Var without correlations for portfolio of derivative securities. J. Futures Mark. 19, 583–602 (1999)
Battalio, R., Schultz, P.: Options and the bubble. J. Financ. 61(5), 2071–2102 (2006)
Bollen, N.P.B., Whaley, R.E.: Does net buying pressure affect the shape of implied volatility functions? J. Financ. 59(2), 711–753 (2004)
Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A.: Classification and Regression Trees. Chapman & Hall/CRC Press, London/Boca Raton (1984)
Cassesse, G., Guidolin, M.: Modelling the MIB30 implied volatility surface. Does market efficiency matter? Int. Rev. Financ. Analy. 15(2), 145–178 (2006)
Cont, R., da Fonseca, J.: Dynamics of implied volatility surfaces. Quantitative Financ. 2(1), 45–60 (2002)
Dumas, B., Fleming, J., Whaley, R.E.: Implied volatility functions: empirical tests. J. Financ. 53(6), 2059–2106 (1998)
Fengler, M.R.: Semiparametric Modeling of Implied Volatility. Springer, Berlin (2005)
Fengler, M.R., Härdle, W.K., Mammen, E.: A semiparametric factor model for implied volatility surface dynamics. J. Financ. Econom. 5(2), 189–218 (2007)
Friedman, J.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29(5), 1189–1232 (2001)
Friedman, J., Hastie, T., Tibshirani, R.: Additive logistic regression: a statistical view of boosting. Ann. Stat. 28(2), 337–407 (2000)
Garcia, R., Luger, R., Renault, E.: Pricing and hedging options with implied asset prices and volatilities. Working Paper, CIRANO, CIREQ and Université de Montréal (2003)
Gonçalves, S., Guidolin, M.: Predictable dynamics in the S&P 500 index options implied volatility surface. J. Bus. 79(3), 1591–1635 (2006)
Gouriéroux, C., Monfort, A., Tenreiro, C.: Nonparametric diagnostics for structural models. Document de travail 9405, CREST, Paris (1994)
Gouriéroux, C., Monfort, A., Tenreiro, C.: Kernel M-estimators and functional residual plots. Document de travail 9546, CREST, Paris (1995)
Hentschel, L.: Errors in implied volatility estimation. J. Financ. Quant. Anal. 38(4), 779–810 (2003)
Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6(2), 327–343 (1993)
Heston, S.L., Nandi, S.: A closed-form GARCH option valuation model. Rev. Financ. Stud. 13(3), 585–625 (2000)
Manaster, S., Rendleman, R.: Option prices as predictors of equilibrium stock prices. J. Financ. 37, 1043–1057 (1982)
Noh, J., Engle, R.F., Kane, A.: Forecasting volatility and option prices of the S&P 500 index. J. Deriv. 2, 17–30 (1994)
Poon, S.-H., Granger, C.W.J.: Forecasting volatility in financial markets: a review. J. Econ. Lit. 41(2), 478–539 (2003)
Rosenberg, J.: Implied volatility functions: a reprise. J. Deriv. 7, 51–64 (2000)
Shimko, D.: Bounds of probability. Risk 6(4), 33–37 (1993)
Skiadopoulos, G.S., Hodges, S.D., Clewlow, L.: The dynamics of the S&P 500 implied volatility surface. Rev. Deriv. Res. 3(3), 263–282 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Audrino, F., Colangelo, D. Semi-parametric forecasts of the implied volatility surface using regression trees. Stat Comput 20, 421–434 (2010). https://doi.org/10.1007/s11222-009-9134-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-009-9134-y