Subleading correction to the Asian options volatility in the Black-Scholes model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913612731252736 |
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| author | Pirjol, Dan |
| author_facet | Pirjol, Dan |
| contents | The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the subleading $O(T)$ correction to this implied volatility, using an asymptotic expansion for the Hartman-Watson distribution. The result is used to compute subleading corrections to Asian options prices in a small maturity expansion, sharpening the leading order result obtained using large deviations theory. We demonstrate good numerical agreement with precise benchmarks for Asian options pricing in the Black-Scholes model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subleading correction to the Asian options volatility in the Black-Scholes model Pirjol, Dan Mathematical Finance Probability The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the subleading $O(T)$ correction to this implied volatility, using an asymptotic expansion for the Hartman-Watson distribution. The result is used to compute subleading corrections to Asian options prices in a small maturity expansion, sharpening the leading order result obtained using large deviations theory. We demonstrate good numerical agreement with precise benchmarks for Asian options pricing in the Black-Scholes model. |
| title | Subleading correction to the Asian options volatility in the Black-Scholes model |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2407.05142 |