The bandwidth selection in connection to option implied volatility extraction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F15%3A86094768" target="_blank" >RIV/61989100:27510/15:86094768 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985556:_____/15:00452192

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The bandwidth selection in connection to option implied volatility extraction

Popis výsledku v původním jazyce

Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there is no need to look for a model to price liquid exchange traded options, since their price is generally accepted by the demand and supply, for illiquid or even exotic options new efficient models are still developed. The current market practice is to obtain the implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. Since the BS model at one time moment can be related to a large set of IVs as given by different parameters (maturity/moneyness relation) of tradable options leading to IV curve or surface. Since there is no continuum of options with various parameters, the curve / surface must be obtained by suitable smoothing and interpolation. However, it can bring an arbitrage opportunity, if no-arbitrage conditions on state price density (SPD) are ignored. The focus of this paper is to study the behavior of IV and SPD for several kernel functions and with respect to different choices of bandwidth parameter h. Specifically, we show several interesting implications of the change of h on the violation of no arbitrage condition and the total area of SPD under zero.

Název v anglickém jazyce

The bandwidth selection in connection to option implied volatility extraction

Popis výsledku anglicky

Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there is no need to look for a model to price liquid exchange traded options, since their price is generally accepted by the demand and supply, for illiquid or even exotic options new efficient models are still developed. The current market practice is to obtain the implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. Since the BS model at one time moment can be related to a large set of IVs as given by different parameters (maturity/moneyness relation) of tradable options leading to IV curve or surface. Since there is no continuum of options with various parameters, the curve / surface must be obtained by suitable smoothing and interpolation. However, it can bring an arbitrage opportunity, if no-arbitrage conditions on state price density (SPD) are ignored. The focus of this paper is to study the behavior of IV and SPD for several kernel functions and with respect to different choices of bandwidth parameter h. Specifically, we show several interesting implications of the change of h on the violation of no arbitrage condition and the total area of SPD under zero.

Druh

D - Stať ve sborníku

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Liberec Economic Forum 2015 : proceedings of the 12th international conference : 16th - 17th September 2015, Liberec, Czech Republic, EU

ISBN

978-80-7494-225-9

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

201-208

Název nakladatele

Technical University of Liberec

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

16. 9. 2015

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000365053000020