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On Extracting Information Implied in Options

Matthias Fengler, M. Benko, Wolfgang K. Härdle & M. Kopa

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abstract 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.
   
type journal paper
   
keywords Implied volatility, Nonparametric regression
   
language English
kind of paper journal article
date of appearance 28-6-2007
journal Computational Statistics
publisher Springer-Verlag
ISSN 0943-4062
DOI 10.1007/s00180-007-0061-0
volume of journal 22
number of issue 4
page(s) 543-553
review double-blind review
   
citation Fengler, M., Benko, M., Härdle, W. K., & Kopa, M. (2007). On Extracting Information Implied in Options. Computational Statistics, 22(4), 543-553, DOI:10.1007/s00180-007-0061-0.