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2005-09-14Masterarbeit DOI: 10.18452/14056
Application of Smoothing Techniques to Implied Volatility
dc.contributor.authorZeng, Jin
dc.date.accessioned2017-06-18T02:10:57Z
dc.date.available2017-06-18T02:10:57Z
dc.date.created2006-03-20
dc.date.issued2005-09-14none
dc.identifier.urihttp://edoc.hu-berlin.de/18452/14708
dc.description.abstractImplied volatility is an important element in risk management and option pricing. Black-Scholes model assumes a constant volatility, however, the evidence from financialmarket shows that the volatility is not constant but change with strike and time tomaturity. In this paper, the time to maturity is fixed and we will construct the implied volatility function of strike or moneyness. We can use regression method for estimation, but the data from financial market contains some noise and we need to apply smoothing techniques to estimate this implied volatility function. The standard non- and semiparametric regression methods don’t guarantee the resulting IV functions are arbitrage free, so we will insert our estimation result to Black and Scholes model and calculate the state price density (SPD). In a Black-Scholes model it is lognormal distribution with constant volatility parameter. In practice as volatility changes the distribution deviates from log-normality. We estimate volatilities and SPDs using EUREX option data on the DAX index by using different smoothing techniques. Our estimation will be carried out through the strike direction and moneyness direction. We will briefly introduce Local polynomials as one method. The most important smoothing techniques we will applied in this paper is B-splines, with the usage of roughness penalty, which allows a flexible choice on the degree of smoothness, and is promising for future research work on the arbitrage free constraint of implied volatility.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
dc.subjectB-splineseng
dc.subjectimplied volatilityeng
dc.subjectstate price densityeng
dc.subjectroughness penaltyeng
dc.subjectlinear differential operatoreng
dc.subject.ddc310 Statistik
dc.subject.ddc330 Wirtschaft
dc.titleApplication of Smoothing Techniques to Implied Volatility
dc.typemasterThesis
dc.identifier.urnurn:nbn:de:kobv:11-10061421
dc.identifier.doihttp://dx.doi.org/10.18452/14056
dc.contributor.refereeHärdle, Wolfgang
dc.subject.dnb15 Statistik
dc.subject.dnb17 Wirtschaft
local.edoc.pages79
local.edoc.type-nameMasterarbeit
local.edoc.institutionWirtschaftswissenschaftliche Fakultät

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