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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.
    2. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    3. Kullmann, L & Töyli, J & Kertesz, J & Kanto, A & Kaski, K, 1999. "Characteristic times in stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 98-110.
    4. Andrew Matacz, 2000. "Financial Modeling And Option Theory With The Truncated Levy Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 143-160.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Palágyi, Zoltán & Mantegna, Rosario N., 1999. "Empirical investigation of stock price dynamics in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 132-139.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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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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