Sima Mashayekhi; Seyed Nourollah Mousavi
Abstract
This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates ...
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This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates both the efficacy of the number of invested stocks and the abnormal increase of volatility during a financial crisis for hedging pur- poses and the financial risk management. To evaluate the performance of these models, we use numerical methods such as finite difference schemes and Monte-Carlo simulation with antithetic variate variance reduction tech- nique. Our results show that the generalized Liu and Young model outper- forms the classic Black-Scholes model in terms of accuracy, especially in high volatile illiquid markets. Additionally, we find that the finite differ- ence schemes are more efficient and faster than the Monte-Carlo simulation in this model. Based on these findings, we recommend using the general- ized Liu and Young model with finite difference schemes for the European options and Greeks valuing in high volatile illiquid markets.
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.
