Document Type : Original Article
Authors
1 Department of Statistics, NT.C., Islamic Azad University, Tehran, Iran.
2 Department of Accounting & Management, Shahr.C., Islamic Azad University, Shahriar, Iran.
Abstract
The main objective of this research is to estimate and simulate the upper and lower bounds of Asian option prices using the MCMC method and to evaluate the efficiency of this approach in improving pricing models and contributing to the development of financial markets. Therefore, this study falls within the field of numerical analysis and computational finance. In this research, the pricing bounds of Asian options are determined using the MCMC simulation method. The statistical population consists of possible price paths of the underlying asset, which are modeled under a specified stochastic process, such as geometric Brownian motion, and the resulting outcomes are analyzed. In this context, explicit formulas are provided for several Lévy models, including the Kou model, the Merton model, and the NIG model. In the next stage, the results obtained from each of the Kou, Merton, and Normal Inverse Gaussian models are compared with the results of the MC simulation. The methods applied in this study include the upper bound method and the lower bound method. The results indicate that the lower bound is faster and more accurate than the upper bound. In particular, the numerical analysis shows that the lower bound introduced in this study can be computed very quickly and provides a high level of accuracy. Furthermore, for all considered models, the upper bound is computed at a reasonably fast rate; however, it is slower than the lower bound, which involves a single integral.
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