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Idősor-modellezés és opcióárazás csonkolt Lévy-eloszlással
[Time-series modelling and option pricing with a truncated Lévy distribution]

Author

Listed:
  • Janecskó, Balázs

Abstract

Statisztikusok és pénzügyi adatelemzők számára jól ismert empirikus tény, hogy a pénzügyi ingadozások természete eltér a klasszikus, normális (Gauss) eloszláson alapuló leírástól. A pénzügyi matematika, illetve az elméleti pénzügyi irodalom mégis paradigmaként kezeli tovább a normális megközelítést egyszerűsége és például az opcióárazási vagy portfólióoptimalizálási feladatban mutatott elegáns analitikus tulajdonságai miatt. E cikk célja az árfolyam-ingadozások realisztikusabb statisztikai képének bemutatása, valamint egy erre a modellre alapított opcióárazási megközelítés felvázolása. Nem célunk matematikai és technikai részleteket közölni ezeket a hivatkozásaink alapján részletesen át lehet tanulmányozni , hanem inkább az új modell szemléletes megvilágítására, illetve gyakorlati alkalmazhatóságának igazolására koncentrálunk. Árfolyam-ingadozási adatainkat a napi BUX záróárfolyam-idősorból származtattuk, az új statisztikai modell illesztését a napi BUX-hozamok példáján illusztráljuk, és az opcióárazási feladat megoldását a BUX-indexre vonatkozó európai call opciókra mutatjuk be. A bemutatott új modell a csonkolt Lévy-modell vonzó tulajdonsága, hogy három paraméteren keresztül képes az ingadozások széles tartományában pontosan leírni a fluktuációk valószínűségét, továbbá a ,,skála, farokvastagsági és csonkolási paramétereknek" szemléletes jelentés is tulajdonítható. Az új modell általában a piaci kockázatkezelésnek is hasznos eszköze lehet, különösen amiatt, hogy a gyakorlatban megfigyelt extrém események valószínűségére is reális számokat ad.

Suggested Citation

  • Janecskó, Balázs, 2000. "Idősor-modellezés és opcióárazás csonkolt Lévy-eloszlással [Time-series modelling and option pricing with a truncated Lévy distribution]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 899-917.
    • Handle: RePEc:ksa:szemle:353
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    References listed on IDEAS

    as
    1. Jánosi, Imre M & Janecskó, Balázs & Kondor, Imre, 1999. "Statistical analysis of 5 s index data of the Budapest Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 111-124.
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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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