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Asymptotic pricing of short-maturity near-the-money options in stochastic volatility models

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  • Kim, Jaehyun
  • Shin, Cheolmin
  • Park, Hyungbin

Abstract

This work introduces an implied local volatility, a novel type of implied volatility, for derivative pricing in stochastic volatility models. Unlike the traditional implied volatility, which is a constant derived from the Black–Scholes model, the implied local volatility is a time-variable function inferred from the local volatility model. We derive a short-maturity at-the-money asymptotic expansion for the implied local volatility using a partial differential equation approach. Two types of stochastic volatility models are covered: the Heston model for stock prices and the SABR model for forward prices. For both types of stochastic volatility models, we estimate short-maturity at-the-money Asian call prices and conclude that the implied local volatility closely approximates the true values.

Suggested Citation

  • Kim, Jaehyun & Shin, Cheolmin & Park, Hyungbin, 2026. "Asymptotic pricing of short-maturity near-the-money options in stochastic volatility models," Finance Research Letters, Elsevier, vol. 87(C).
    • Handle: RePEc:eee:finlet:v:87:y:2026:i:c:s1544612325021750
    DOI: 10.1016/j.frl.2025.108922
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
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