Abstract:
This work is devoted to the study of the asymptotic behavior of the probability density function of stock prices within models with stochastic volatility. The main focus is on generalizing previously known results for the one-factor Heston model to more complex cases, including multivariate models. The research methodology is based on the use of affine principles, which allow analyzing the necessary aspects of asymptotics through solving corresponding Riccati equations near the critical point. The application of high-order Euler estimates ensures accuracy in calculations and robustness of conclusions. Additionally, the method of steepest descent combined with Tauber's principle is used, providing an opportunity to extract precise data about the asymptote of the original function from the analysis of its transformation near the critical point. This allows a deeper understanding of the structure of probability density functions in the context of complex stochastic systems. The obtained results are important for the development of the theory of stochastic differential equations and can find applications in various fields such as financial mathematics and econometrics.
Keywords:asymptotic formula for the stock of an option, multidimensional Heston model, Mellin transform.
UDC:
517.9 BBK:
22.161.6
Received: December 3, 2024 Published: July 31, 2025
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