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Asymptotic expansion for some local volatility models arising in finance

Author

Listed:
  • Sergio Albeverio

    (University of Bonn)

  • Francesco Cordoni

    (University of Verona)

  • Luca Persio

    (University of Verona)

  • Gregorio Pellegrini

    (Financial and Credit Risk, Gruppo Generali Italia Spa)

Abstract

In this paper, we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders. Moreover, we perform a detailed numerical analysis, with accuracy comparisons, of the obtained results by means of the standard Monte Carlo technique as well as exploiting the Polynomial Chaos Expansion approach.

Suggested Citation

  • Sergio Albeverio & Francesco Cordoni & Luca Persio & Gregorio Pellegrini, 2019. "Asymptotic expansion for some local volatility models arising in finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 527-573, December.
    • Handle: RePEc:spr:decfin:v:42:y:2019:i:2:d:10.1007_s10203-019-00247-w
    DOI: 10.1007/s10203-019-00247-w
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    References listed on IDEAS

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    Cited by:

    1. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    2. Xuekang Zhang & Shounian Deng & Weiyin Fei, 2023. "Nonparametric Estimation of Trend for Stochastic Processes Driven by G-Brownian Motion with Small Noise," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.

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    More about this item

    Keywords

    Local volatility models; Small noise asymptotic expansions; Corrections to the Black–Scholes type models; Jump-diffusion models; Polynomial drift; Exponential drift; Polynomial Chaos Expansion method; Monte Carlo techniques;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • 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
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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