Some asymptotics for short maturity Asian options.
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| Title: | Some asymptotics for short maturity Asian options. |
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| Authors: | Shoshi, Humayra1 (AUTHOR), SenGupta, Indranil2,3 (AUTHOR) isengupt@fiu.edu |
| Source: | Stochastic Models. 2025, Vol. 41 Issue 3, p356-382. 27p. |
| Subjects: | Asymptotic analysis, Large deviation theory, Financial instruments, Derivative securities, Market value |
| Abstract: | Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this article, we use the large deviations theory for the analysis of short-maturity Asian options. We present a constant volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this article, we use the large deviations theory for the analysis of short-maturity Asian options. We present a constant volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 15326349 |
| DOI: | 10.1080/15326349.2024.2394818 |
