Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912055935631360 |
|---|---|
| author | Choi, Jaehyuk Huh, Jeonggyu Su, Nan |
| author_facet | Choi, Jaehyuk Huh, Jeonggyu Su, Nan |
| contents | Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton-Raphson algorithm, whose convergence is slow for extreme option prices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08758 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding Choi, Jaehyuk Huh, Jeonggyu Su, Nan Mathematical Finance Computational Finance Pricing of Securities 91G20, 91G60 Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton-Raphson algorithm, whose convergence is slow for extreme option prices. |
| title | Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding |
| topic | Mathematical Finance Computational Finance Pricing of Securities 91G20, 91G60 |
| url | https://arxiv.org/abs/2302.08758 |