Analytic approximation for Bachelier option prices and applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911663865724928 |
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| author | Alòs, Elisa Burés, Òscar |
| author_facet | Alòs, Elisa Burés, Òscar |
| contents | It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (non-integer) powers of the future mean volatility. As an a application, we use it as a control variate to reduce the variance of Monte Carlo option prices in the correlated case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02040 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytic approximation for Bachelier option prices and applications Alòs, Elisa Burés, Òscar Computational Finance 91G20, 91G60 It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (non-integer) powers of the future mean volatility. As an a application, we use it as a control variate to reduce the variance of Monte Carlo option prices in the correlated case. |
| title | Analytic approximation for Bachelier option prices and applications |
| topic | Computational Finance 91G20, 91G60 |
| url | https://arxiv.org/abs/2605.02040 |