Computational Statistics

, Volume 22, Issue 4, pp 543–553 | Cite as

On extracting information implied in options

  • M. BenkoEmail author
  • M. Fengler
  • W. Härdle
  • M. Kopa
Original Paper


Options are financial instruments with a payoff depending on future states of the underlying asset. Therefore option markets contain information about expectations of the market participants about market conditions, e.g. current uncertainty on the market and corresponding risk. A standard measure of risk calculated from plain vanilla options is the implied volatility (IV). IV can be understood as an estimate of the volatility of returns in future period. Another concept based on the option markets is the state-price density (SPD) that is a density of the future states of the underlying asset. From raw data we can recover the IV function by nonparametric smoothing methods. Smoothed IV estimated by standard techniques may lead to a non-positive SPD which violates no arbitrage criteria. In this paper, we combine the IV smoothing with SPD estimation in order to correct these problems. We propose to use the local polynomial smoothing technique. The elegance of this approach is that it yields all quantities needed to calculate the corresponding SPD. Our approach operates only on the IVs—a major improvement comparing to the earlier multi-step approaches moving through the Black–Scholes formula from the prices to IVs and vice-versa.


Implied volatility Nonparametric regression 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bertsekas D (1999) Nonlinear programming. Athena Scientific, BelmontzbMATHGoogle Scholar
  2. Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:637–654CrossRefGoogle Scholar
  3. Breeden D, Litzenberger R (1978) Price of state-contingent claims implicit in options prices. J Bus 51:621–651CrossRefGoogle Scholar
  4. Britten-Jones M, Neuberger A (2000) Option prices, implied price process and stochastic volatility. J Fin 55(2):839–866CrossRefGoogle Scholar
  5. Brockhaus O, Farkas M, Ferraris A, Long D, Overhaus M (2000) Equity derivatives and market risk models. Risk Books, LondonGoogle Scholar
  6. Brunner B, Hafner R (2003) Arbitrage-free estimation of the risk-neutral density from the implied volatility smile. J Comput Fin 7:75–106Google Scholar
  7. Cont R, da Fonseca J (2002) The dynamics of implied volatility surfaces. J Quant Fin 2(1):45–60CrossRefMathSciNetGoogle Scholar
  8. Edwards R, Magee J (1966) Technical analysis of stock trends, 5th edn. John Magee, BostonGoogle Scholar
  9. Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Chapman and Hall, LondonzbMATHGoogle Scholar
  10. Fengler M (2005a) Arbitrage-free smoothing of the implied volatility surface. Working paper 2005-019, SFB 649, Humboldt-Universität zu BerlinGoogle Scholar
  11. Fengler M (2005b) Semiparametric modeling of implied volatility. Springer, BerlinzbMATHGoogle Scholar
  12. Fengler M, Härdle W, Villa P (2003) The dynamics of implied volatilities: a common principle components approach. Rev Deriv Res 6:179–202zbMATHCrossRefGoogle Scholar
  13. Harrison J, Kreps D (1979) Martingales and stochastic integral in the theory of continuous trading. Stochast Process Appl 11:215–260CrossRefGoogle Scholar
  14. Harrison J, Pliska S (1981) Martingales and arbitrage in multiperiod securities markets. J Econ Theory 20:381–408CrossRefGoogle Scholar
  15. Härdle W (1990) Applied nonparametric regression. Cambridge University Press, CambridgezbMATHGoogle Scholar
  16. Hentschel L (2003) Errors in implied volatility estimation. J Fin Quant Anal 38:779–810Google Scholar
  17. Jackwerth JC (2004) Option-implied risk neutral distributions and risk aversion, Research Foundation of AIMR, Charlotteville, USAGoogle Scholar
  18. Hull CJ, White A (1987) The pricing of options on assets with stochastic volatilities. J Fin 42:281–300CrossRefGoogle Scholar
  19. Kahale N (2004) An arbitrage-free interpolation of volatilities. RISK 17(5):102–106Google Scholar
  20. Murphy J (1986) Technical analysis of the futures market. New York Institute of Finance, New YorkGoogle Scholar
  21. Musiela M, Rutkowski M (1997) Martingale methods in financial modelling. Springer, HeidelbergzbMATHGoogle Scholar
  22. Rebonato R (1999) Volatility and correlation. Wiley series in financial in financial ingeniering. Wiley, New YorkGoogle Scholar
  23. Spokoiny V (2006) Local parametric methods in nonparametric estimation. Springer, HeidelbergGoogle Scholar
  24. Shimko D (1993) Bounds on probability. RISK 6(4):33–37Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Charles UniversityPragueCzech Republic

Personalised recommendations