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 theleast squares fuzzy regression method of Savic and Pedrycz [27]and to the hybrid method of Ishibuchi and Nii[11].

A comparison of fuzzy regression methods for the estimation of the implied volatility smile function / Muzzioli, Silvia; Ruggieri, A.; De Baets, B.. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 266:(2015), pp. 131-143. [10.1016/j.fss.2014.11.015]

A comparison of fuzzy regression methods for the estimation of the implied volatility smile function

MUZZIOLI, Silvia;
2015

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 theleast squares fuzzy regression method of Savic and Pedrycz [27]and to the hybrid method of Ishibuchi and Nii[11].
2015
24-nov-2014
266
131
143
A comparison of fuzzy regression methods for the estimation of the implied volatility smile function / Muzzioli, Silvia; Ruggieri, A.; De Baets, B.. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 266:(2015), pp. 131-143. [10.1016/j.fss.2014.11.015]
Muzzioli, Silvia; Ruggieri, A.; De Baets, B.
File in questo prodotto:
File Dimensione Formato  
PUBBLICAZIONE N.4 FSS 2015.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 695.19 kB
Formato Adobe PDF
695.19 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1061262
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 43
  • ???jsp.display-item.citation.isi??? 38
social impact