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Short-Time Implied Volatility In Exponential Lévy Models

Author

Listed:
  • ERIK EKSTRÖM

    (Department of Mathematics, Uppsala University, Box 480, SE-75106 Uppsala, Sweden)

  • BING LU

    (Department of Mathematics, Uppsala University, Box 480, SE-75106 Uppsala, Sweden)

Abstract

We show that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process. When such jumps do not exist, the implied volatility converges to the volatility of the Gaussian component of the underlying Lévy process as the time to maturity tends to zero. These results are proved by comparing the short-time asymptotics of the Black–Scholes price with explicit formulas for upper and lower bounds of option prices in exponential Lévy models.

Suggested Citation

  • Erik Ekström & Bing Lu, 2015. "Short-Time Implied Volatility In Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-14.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:04:n:s0219024915500259
    DOI: 10.1142/S0219024915500259
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