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Un nuovo algoritmo di inversione della distribuzione normale standardizzata e sue applicazioni finanziarie

Author

Listed:
  • Maria Giuseppina Bruno

    (Department of Methods and Models for Economics, Territory and Finance MEMOTEF, Sapienza University of Rome (Italy))

  • Antonio Grande

    (Department of Methods and Models for Economics, Territory and Finance MEMOTEF, Sapienza University of Rome (Italy))

Abstract

Nelle applicazioni finanziarie del metodo Montecarlo e Quasi–Montecarlo, uno dei problemi più comuni è il campionamento da una data distribuzione cumulata. In questo documento, tra i diversi approcci, ci riferiamo al metodo della “Trasformata inversa†e proponiamo un nuovo algoritmo per eseguire l’inversione. Mostriamo in particolare un’applicazione del suddetto algoritmo per calcolare l’inversa della funzione di ripartizione normale standardizzata e valutare opzioni ?nanziarie su un sottostante con rendimenti normali. L’algoritmo proposto è implementabile su personal computer tradizionali ed è paragonabile per velocità ed errore di approssimazione agli altri presenti in letteratura. Un suo ulteriore vantaggio è quello di essere facilmente generalizzabile ad altre distribuzioni ed alle relative inverse. In questo modo è possibile impiegarlo per la valutazione delle opzioni ?nanziarie in ipotesi diverse riguardo la dinamica del sottostante

Suggested Citation

  • Maria Giuseppina Bruno & Antonio Grande, "undated". "Un nuovo algoritmo di inversione della distribuzione normale standardizzata e sue applicazioni finanziarie," Working Papers 131/14, Sapienza University of Rome, Metodi e Modelli per l'Economia, il Territorio e la Finanza MEMOTEF.
    • Handle: RePEc:rsq:wpaper:30/14
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    References listed on IDEAS

    as
    1. J. D. Beasley & S. G. Springer, 1977. "The Percentage Points of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 118-121, March.
    2. Masaglia, George & Zaman, Arif & Marsaglia, John C. W., 1994. "Rapid evaluation of the inverse of the normal distribution function," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 259-266, March.
    3. Brent, Richard P., 2004. "Note on Marsaglia's Xorshift Random Number Generators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i05).
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Maria Giuseppina Bruno & Antonio Grande, "undated". "Pricing arithmetic average options and basket options using Monte Carlo and Quasi-Monte methods," Working Papers 143/15, Sapienza University of Rome, Metodi e Modelli per l'Economia, il Territorio e la Finanza MEMOTEF.

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    More about this item

    Keywords

    : Inverse of a Distribution; Montecarlo and Quasi–Montecarlo Methods; Financial Options Evaluation; Algorithm.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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