Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model. Similar results re available previously only in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as  essentially use only Ito's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. As a by-product  also show that a ll-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate; and it performs ll even in the case of low volatilities.
['Ning Cai', 'Steven Kou']
I am writing a research paper on a idea Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model
[{"from": "human", "value": "I am writing a research paper on a idea Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model. Similar results re available previously only in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as  essentially use only Ito's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. As a by-product  also show that a ll-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate; and it performs ll even in the case of low volatilities."}]