Azadeh Ghasemifard; Ali Valinejad
Abstract
In this article, we discuss the numerical implementation of the Multilevel Monte-Carlo (MLMC) scheme for option pricing within the Heston asset model. The Heston model is a stochastic volatility model that captures the dynamics of the underlying asset price and its volatility. The MLMC method is a variance ...
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In this article, we discuss the numerical implementation of the Multilevel Monte-Carlo (MLMC) scheme for option pricing within the Heston asset model. The Heston model is a stochastic volatility model that captures the dynamics of the underlying asset price and its volatility. The MLMC method is a variance reduction technique that exploits the difference between two consecutive levels of discretization to estimate the expected value of a quantity of interest. We begin by providing an overview of the MLMC method, followed by an introduction to the weak methods used to approximate the Heston model. Weak methods are numerical schemes that preserve the distributional properties of the solution, rather than its pathwise behavior. Subsequently, we present the results of some numerical experiments conducted to evaluate the performance of the approach. Two different cases are surveyed.
Ali Bolfake; Seyed Nourollah Mousavi; Sima Mashayekhi
Abstract
This paper proposes a new approach to pricing European options using deep learning techniques under the Heston and Bates models of random fluctuations. The deep learning network is trained with eight input hyper-parameters and three hidden layers, and evaluated using mean squared error, correlation coefficient, ...
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This paper proposes a new approach to pricing European options using deep learning techniques under the Heston and Bates models of random fluctuations. The deep learning network is trained with eight input hyper-parameters and three hidden layers, and evaluated using mean squared error, correlation coefficient, coefficient of determination, and computation time. The generation of data was accomplished through the use of Monte Carlo simulation, employing variance reduction techniques. The results demonstrate that deep learning is an accurate and efficient tool for option pricing, particularly under challenging pricing models like Heston and Bates, which lack a closed-form solution. These findings highlight the potential of deep learning as a valuable tool for option pricing in financial markets.
