Asymptotic Analysis of Implied Volatility Under Stochastic Volatility Jump-Diffusion Models
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| Formato: | Recurso digital |
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2025
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| _version_ | 1866901983630196736 |
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| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | In this paper, we investigate the asymptotic behavior of implied volatility in financial markets under stochastic volatility jump-diffusion models. We derive approximations for the implied volatility surface when the time to maturity approaches zero and infinity. We analyze the impact of jumps in both the asset price and the volatility process on the short-term and long-term implied volatility smiles and skews. The study employs advanced techniques from stochastic calculus, including martingale theory and asymptotic expansion methods, to obtain closed-form approximations. We compare our theoretical results with numerical simulations to demonstrate the accuracy of our asymptotic formulas. The findings provide valuable insights for option pricing, risk management, and volatility trading strategies. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17830217 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Asymptotic Analysis of Implied Volatility Under Stochastic Volatility Jump-Diffusion Models Revista, Zen MATH, 10 In this paper, we investigate the asymptotic behavior of implied volatility in financial markets under stochastic volatility jump-diffusion models. We derive approximations for the implied volatility surface when the time to maturity approaches zero and infinity. We analyze the impact of jumps in both the asset price and the volatility process on the short-term and long-term implied volatility smiles and skews. The study employs advanced techniques from stochastic calculus, including martingale theory and asymptotic expansion methods, to obtain closed-form approximations. We compare our theoretical results with numerical simulations to demonstrate the accuracy of our asymptotic formulas. The findings provide valuable insights for option pricing, risk management, and volatility trading strategies. |
| title | Asymptotic Analysis of Implied Volatility Under Stochastic Volatility Jump-Diffusion Models |
| url | https://doi.org/10.5281/zenodo.17830217 |