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Short-time implied volatility of additive normal tempered stable processes

Author

Listed:
  • Michele Azzone

    (Politecnico di Milano
    European Central Bank)

  • Roberto Baviera

    (Politecnico di Milano)

Abstract

Empirical studies have emphasized that the equity implied volatility is characterized by a negative skew inversely proportional to the square root of the time-to-maturity. We examine the short-time-to-maturity behavior of the implied volatility smile for pure jump exponential additive processes. An excellent calibration of the equity volatility surfaces has been achieved by a class of these additive processes with power-law scaling. The two power-law scaling parameters are $$\beta $$ β , related to the variance of jumps, and $$\delta $$ δ , related to the smile asymmetry. It has been observed, in option market data, that $$\beta =1$$ β = 1 and $$\delta =-1/2$$ δ = - 1 / 2 . In this paper, we prove that the implied volatility of these additive processes is consistent, in the short-time, with the equity market empirical characteristics if and only if $$\beta =1$$ β = 1 and $$\delta =-1/2$$ δ = - 1 / 2 .

Suggested Citation

  • Michele Azzone & Roberto Baviera, 2024. "Short-time implied volatility of additive normal tempered stable processes," Annals of Operations Research, Springer, vol. 336(1), pages 93-126, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-04894-y
    DOI: 10.1007/s10479-022-04894-y
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    References listed on IDEAS

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    More about this item

    Keywords

    Additive process; Volatility surface; Skew; Small-time; Calibration;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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