On extracting information implied in options
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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.
KeywordsImplied volatility Nonparametric regression
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- Brockhaus O, Farkas M, Ferraris A, Long D, Overhaus M (2000) Equity derivatives and market risk models. Risk Books, LondonGoogle Scholar
- 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
- Edwards R, Magee J (1966) Technical analysis of stock trends, 5th edn. John Magee, BostonGoogle Scholar
- Fengler M (2005a) Arbitrage-free smoothing of the implied volatility surface. Working paper 2005-019, SFB 649, Humboldt-Universität zu BerlinGoogle Scholar
- Hentschel L (2003) Errors in implied volatility estimation. J Fin Quant Anal 38:779–810Google Scholar
- Jackwerth JC (2004) Option-implied risk neutral distributions and risk aversion, Research Foundation of AIMR, Charlotteville, USAGoogle Scholar
- Kahale N (2004) An arbitrage-free interpolation of volatilities. RISK 17(5):102–106Google Scholar
- Murphy J (1986) Technical analysis of the futures market. New York Institute of Finance, New YorkGoogle Scholar
- Rebonato R (1999) Volatility and correlation. Wiley series in financial in financial ingeniering. Wiley, New YorkGoogle Scholar
- Spokoiny V (2006) Local parametric methods in nonparametric estimation. Springer, HeidelbergGoogle Scholar
- Shimko D (1993) Bounds on probability. RISK 6(4):33–37Google Scholar