Innovative Solutions for Hedge Errors in the Black-Scholes Model

Table of Links Abstract and 1. Introduction 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution Literature Review Methodology 3.1 Model Assumption 3.2 Theorems and Model Discussion Result Analysis Conclusion and References 1.6 OUR CONTRIBUTION In our research paper, we significantly contribute by introducing an innovative method for approximating hedge errors in the Black-Scholes option pricing model. Our approach leverages asymptotic techniques to enhance the accuracy of finite difference methods commonly used in options pricing. Furthermore, we extend our investigation to incorporate variance reduction techniques within the Monte Carlo simulation. By integrating these methods, we aim to mitigate the computational burden associated with simulating option prices while maintaining high levels of precision. Through rigorous experimentation and analysis, we demonstrate the effectiveness of our proposed framework in reducing variance and improving the efficiency of option pricing simulations. Our contribution lies not only in the development of novel methodologies but also in their practical applicability. We provide comprehensive theoretical insights supported by empirical evidence, showcasing the superiority of our approach compared to traditional methods. This advancement holds significant implications for financial practitioners, enabling more accurate and efficient pricing and hedging of options in real-world scenarios. In summary, our research presents a valuable contribution to the field of quantitative finance by offering innovative solutions to enhance the accuracy and efficiency of option pricing models. Through the integration of asymptotic techniques and variance reduction methods within Monte Carlo simulation, we provide a comprehensive framework for addressing hedge errors in the Black-Scholes model, thus advancing the state-of-the-art in financial modeling and analysis. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Option Pricing 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.3 Finite Difference 1.4 The Black-Schole Model 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution 1.6 Our Contribution Literature Review Methodology Literature Review Literature Review Literature Review Methodology Methodology 3.1 Model Assumption 3.1 Model Assumption 3.2 Theorems and Model Discussion 3.2 Theorems and Model Discussion Result Analysis Conclusion and References Result Analysis Result Analysis Result Analysis Conclusion and References Conclusion and References Conclusion and References 1.6 OUR CONTRIBUTION In our research paper, we significantly contribute by introducing an innovative method for approximating hedge errors in the Black-Scholes option pricing model. Our approach leverages asymptotic techniques to enhance the accuracy of finite difference methods commonly used in options pricing. Furthermore, we extend our investigation to incorporate variance reduction techniques within the Monte Carlo simulation. By integrating these methods, we aim to mitigate the computational burden associated with simulating option prices while maintaining high levels of precision. Through rigorous experimentation and analysis, we demonstrate the effectiveness of our proposed framework in reducing variance and improving the efficiency of option pricing simulations. Our contribution lies not only in the development of novel methodologies but also in their practical applicability. We provide comprehensive theoretical insights supported by empirical evidence, showcasing the superiority of our approach compared to traditional methods. This advancement holds significant implications for financial practitioners, enabling more accurate and efficient pricing and hedging of options in real-world scenarios. In summary, our research presents a valuable contribution to the field of quantitative finance by offering innovative solutions to enhance the accuracy and efficiency of option pricing models. Through the integration of asymptotic techniques and variance reduction methods within Monte Carlo simulation, we provide a comprehensive framework for addressing hedge errors in the Black-Scholes model, thus advancing the state-of-the-art in financial modeling and analysis. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). Authors: Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv