On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model

2023/08/29 by Elisa Alòs, Alòs, Elisa, Eulàlia Nualart +3 · 1 citation
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2308.15341

openalex publication_date 2023/08/29 · openalex created_date 2023/08/31 · openalex updated_date 2026/07/31

Abstract

In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating Ito's formula we first compute the level of the implied volatility when the maturity converges to zero. Then, we find a short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We apply our general results to the SABR and fractional Bergomi models, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew.

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