arXiv Open Access 2023

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

Elisa Alòs Eulalia Nualart Makar Pravosud

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

q-fin.MF

Penulis (3)

Elisa Alòs

Eulalia Nualart

Makar Pravosud

Format Sitasi

APA MLA BibTeX

Alòs, E., Nualart, E., Pravosud, M. (2023). On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model. https://arxiv.org/abs/2308.15341

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓