Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914787684777984 |
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| author | Pirjol, Dan Zhu, Lingjiong |
| author_facet | Pirjol, Dan Zhu, Lingjiong |
| contents | We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with Lévy jumps, including the exponential Lévy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility Pirjol, Dan Zhu, Lingjiong Pricing of Securities We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with Lévy jumps, including the exponential Lévy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity. |
| title | Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility |
| topic | Pricing of Securities |
| url | https://arxiv.org/abs/2308.15672 |