Abstract
The information content of option prices on the underlying asset has a special importance in finance. In particular, with the use of option implied trees, market participants may price other derivatives, estimate and forecast volatility (see e.g. the volatility index VIX), or higher moments of the underlying asset distribution. A crucial input of option implied trees is the estimation of the smile (implied volatility as a function of the strike price), which boils down to fitting a function to a limited number of existing knots. However, standard techniques require a one-to-one mapping between volatility and strike price, which is not met in the reality of financial markets, where, to a given strike price, two different implied volatilities are usually associated (coming from different types of options: call and put).In this paper we compare the widely used methodology of discarding some implied volatilities and interpolating the remaining knots with cubic splines, to a fuzzy regression approach which does not require an a-priori choice of implied volatilities. To this end, we first extend some linear fuzzy regression methods to a polynomial form and we apply them to the financial problem. The fuzzy regression methods used range from the possibilistic regression method of Tanaka et al. [28], to the least squares fuzzy regression method of Savic and Pedrycz [27] and to the hybrid method of Ishibuchi and Nii [11].
Highlights
The information content of option prices on the underlying asset has a special importance in finance
A crucial input of option implied trees is the estimation of the smile, which boils down to fitting a function to a limited number of existing knots
The way in which implied volatility varies with strike price is referred to as the “smile” effect, since depending on the market under scrutiny, it can be depicted with a smile or a smirk
Summary
The information content of option prices on the underlying asset has a special importance in finance. With the use of option implied trees, market participants may price other derivatives, estimate and forecast volatility (see e.g. the volatility index VIX), or higher moments of the underlying asset distribution. It is market practice to keep the implied volatility of put options for strikes below the current value of the underlying asset and the one of call options for strikes above (those options are called out-ofthe-money, since if exercised they would deliver no positive payoff). The latter market practice is based on the observation that the options retained are the most exchanged and the most informative. The last section concludes and provides some hints for future research
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
