Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign cur...Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.展开更多
The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been app...The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.展开更多
Scientific research and technological innovation are driving modern economies;however,a new form of property rights is required to compensate knowledge workers for their contributions.In 1994,the Science and Technolog...Scientific research and technological innovation are driving modern economies;however,a new form of property rights is required to compensate knowledge workers for their contributions.In 1994,the Science and Technology Bureau of Shenzhen,China implemented a policy to encourage scientists and engineers to develop innovative technologies that would provide them a share of the profits earned from their innovations.This created a new“shared property rights”system.China’s shared property model is so new that the conditions under which it can improve enterprise profits remain unclear.To answer this question,we obtained data from the China Stock Market and Accounting Research database for 904 Chinese enterprises that had implemented shared property rights for the first time between 2009 and 2021 and used a propensity score matching method and econometric models to evaluate their performance.The results indicated that shared property incentives improved corporate financial performance and that benefits increased gradually over time.The new approach showed a stronger positive effect than restricted stock options during the study period.The strength of the incentive was greater for core technical staff than for senior executives,suggesting that scientists,engineers,and computer programmers should be the targets of a shared property rights incentive program.To take full advantage of the new shared property rights institution,enterprise managers should set the implementation period at a reasonable length(5 to 10 years,based on our study results).Enterprises can also test two or more simultaneous approaches that account for the specific needs of each category of workers,based on a careful examination of their current situation and expected or desired future situations.展开更多
In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump inte...In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump intensities of the assets are stochastic.Under the proposed framework,first,we derive the analytical pricing formula for power options by using Fourier transform technique,Esscher transform and characteristic function.Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation.Finally,we provide some sensitivity analysis of the model parameters to power options.Numerical examples show this model is suitable for empirical work in practice.展开更多
The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transf...The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.展开更多
This study investigates an option pricing method called g-pricing based on backward stochastic differential equations combined with deep learning.We adopted a datadriven approach to find a market-appropriate generator...This study investigates an option pricing method called g-pricing based on backward stochastic differential equations combined with deep learning.We adopted a datadriven approach to find a market-appropriate generator of the backward stochastic differential equation,which is achieved by leveraging the universal approximation capabilities of neural networks.Option pricing,which is the solution to the equation,is approximated using a recursive procedure.The empirical results for the S&P 500 index options show that the proposed deep learning g-pricing model has lower absolute errors than the classical Black–Scholes–Merton model for the same forward stochastic differential equations.The g-pricing mechanism has potential applications in option pricing.展开更多
This paper employs the PPO(Proximal Policy Optimization) algorithm to study the risk hedging problem of the Shanghai Stock Exchange(SSE) 50ETF options. First, the action and state spaces were designed based on the cha...This paper employs the PPO(Proximal Policy Optimization) algorithm to study the risk hedging problem of the Shanghai Stock Exchange(SSE) 50ETF options. First, the action and state spaces were designed based on the characteristics of the hedging task, and a reward function was developed according to the cost function of the options. Second, combining the concept of curriculum learning, the agent was guided to adopt a simulated-to-real learning approach for dynamic hedging tasks, reducing the learning difficulty and addressing the issue of insufficient option data. A dynamic hedging strategy for 50ETF options was constructed. Finally, numerical experiments demonstrate the superiority of the designed algorithm over traditional hedging strategies in terms of hedging effectiveness.展开更多
Put options are known to be priced unusually high in the market,which we refer to as the overpriced put puzzle.This study proposes a quantum model(QM)that can explain such high put option prices as fair prices.Startin...Put options are known to be priced unusually high in the market,which we refer to as the overpriced put puzzle.This study proposes a quantum model(QM)that can explain such high put option prices as fair prices.Starting from a stochastic differential equation of stock returns,we convert the Fokker–Planck equation into the Schr鰀inger equation.To model the market force that always draws excess returns back to equilibrium,we specify a diffusion process corresponding to a QM with a delta potential.The results demonstrate that stock returns follow a Laplace distribution and exhibit power law in the tail.We then construct a closed-form solution for European put option pricing,determining that our model better explains the returns of the S&P 500 index and its corresponding put option prices than do geometric Brownian motion-based models.This study has significant implications for investors and risk managers,presenting a model that can potentially improve derivative pricing.Future studies can generalize the model assumptions by introducing asymmetric potential drawing back excess returns to equilibrium.展开更多
From AR-enhanced picture books to eco-friendly smart toys,the items now filling children’s shopping carts are more than just products-they epitomize the transformation of consumption in the new era.
Addressing the issue that flight plans between Chinese city pairs typically rely on a single route,lacking alternative paths and posing challenges in responding to emergencies,this study employs the“quantile-inflecti...Addressing the issue that flight plans between Chinese city pairs typically rely on a single route,lacking alternative paths and posing challenges in responding to emergencies,this study employs the“quantile-inflection point method”to analyze specific deviation trajectories,determine deviation thresholds,and identify commonly used deviation paths.By combining multiple similarity metrics,including Euclidean distance,Hausdorff distance,and sector edit distance,with the density-based spatial clustering of applications with noise(DBSCAN)algorithm,the study clusters deviation trajectories to construct a multi-option trajectory set for city pairs.A case study of 23578 flight trajectories between the Guangzhou airport cluster and the Shanghai airport cluster demonstrates the effectiveness of the proposed framework.Experimental results show that sector edit distance achieves superior clustering performance compared to Euclidean and Hausdorff distances,with higher silhouette coefficients and lower Davies⁃Bouldin indices,ensuring better intra-cluster compactness and inter-cluster separation.Based on clustering results,19 representative trajectory options are identified,covering both nominal and deviation paths,which significantly enhance route diversity and reflect actual flight practices.This provides a practical basis for optimizing flight paths and scheduling,enhancing the flexibility of route selection for flights between city pairs.展开更多
文摘Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.
基金Rami Ahmad El-Nabulsi has received funding from the Czech National Agency of Agricultural 533 Research,project QK22020134“Innovative fisheries management of a large reservoir”.
文摘The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.
基金supported by the National R&D Program China(No.2021xjkk0405).
文摘Scientific research and technological innovation are driving modern economies;however,a new form of property rights is required to compensate knowledge workers for their contributions.In 1994,the Science and Technology Bureau of Shenzhen,China implemented a policy to encourage scientists and engineers to develop innovative technologies that would provide them a share of the profits earned from their innovations.This created a new“shared property rights”system.China’s shared property model is so new that the conditions under which it can improve enterprise profits remain unclear.To answer this question,we obtained data from the China Stock Market and Accounting Research database for 904 Chinese enterprises that had implemented shared property rights for the first time between 2009 and 2021 and used a propensity score matching method and econometric models to evaluate their performance.The results indicated that shared property incentives improved corporate financial performance and that benefits increased gradually over time.The new approach showed a stronger positive effect than restricted stock options during the study period.The strength of the incentive was greater for core technical staff than for senior executives,suggesting that scientists,engineers,and computer programmers should be the targets of a shared property rights incentive program.To take full advantage of the new shared property rights institution,enterprise managers should set the implementation period at a reasonable length(5 to 10 years,based on our study results).Enterprises can also test two or more simultaneous approaches that account for the specific needs of each category of workers,based on a careful examination of their current situation and expected or desired future situations.
文摘In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump intensities of the assets are stochastic.Under the proposed framework,first,we derive the analytical pricing formula for power options by using Fourier transform technique,Esscher transform and characteristic function.Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation.Finally,we provide some sensitivity analysis of the model parameters to power options.Numerical examples show this model is suitable for empirical work in practice.
基金Supported by National Natural Science Foundation of China(11571089,11501164)Natural Science Founda-tion of Hebei Province(A2019205299)+1 种基金the Foundation of Hebei Education Department(ZD2018065,ZD2019053)Hebei Normal University(L2019Z01).
文摘The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian(NIG)process.We first find the risk neutral equivalent martingale measure Q by Esscher transform.Then,using the Fourier transform and its inverse,we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral.In addition,the fast Fourier transform(FFT)algorithm is applied to calculate these pricing formulas.Finally,Shangzheng 50ETF options are chosen to test our results.Estimating the parameters in NIG process by maximum likelihood method,we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton(BSM)ones.
基金supported by Taishan Scholar Project of Shandong Province of China(Grant tstp20240803)the National Key R&D Program of China(Grant No.2023YFA1008903)the Major Fundamental Research Project of Shandong Province of China(Grant No.ZR2023ZD33).
文摘This study investigates an option pricing method called g-pricing based on backward stochastic differential equations combined with deep learning.We adopted a datadriven approach to find a market-appropriate generator of the backward stochastic differential equation,which is achieved by leveraging the universal approximation capabilities of neural networks.Option pricing,which is the solution to the equation,is approximated using a recursive procedure.The empirical results for the S&P 500 index options show that the proposed deep learning g-pricing model has lower absolute errors than the classical Black–Scholes–Merton model for the same forward stochastic differential equations.The g-pricing mechanism has potential applications in option pricing.
基金supported by the Foundation of Key Laboratory of System Control and Information Processing,Ministry of Education,China,Scip20240111Aeronautical Science Foundation of China,Grant 2024Z071108001the Foundation of Key Laboratory of Traffic Information and Safety of Anhui Higher Education Institutes,Anhui Sanlian University,KLAHEI18018.
文摘This paper employs the PPO(Proximal Policy Optimization) algorithm to study the risk hedging problem of the Shanghai Stock Exchange(SSE) 50ETF options. First, the action and state spaces were designed based on the characteristics of the hedging task, and a reward function was developed according to the cost function of the options. Second, combining the concept of curriculum learning, the agent was guided to adopt a simulated-to-real learning approach for dynamic hedging tasks, reducing the learning difficulty and addressing the issue of insufficient option data. A dynamic hedging strategy for 50ETF options was constructed. Finally, numerical experiments demonstrate the superiority of the designed algorithm over traditional hedging strategies in terms of hedging effectiveness.
基金supported by the International Joint Research Grant by Yonsei Graduate School(Kwangwon Ahn)the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(RS-2025-16067531:Kwangwon Ahn)+2 种基金the NRF of Korea grant funded by the Korea government(MSIT)(2020R1A2C1A01005949,RS-2023-00217705:Taeyoung Park)the MSIT(Ministry of Science and ICT)Korea,under the ICAN(ICT Challenge and Advanced Network of HRD)support program(RS-2023-00259934:Taeyoung Park)supervised by the IITP(Institute for Information&Communications Technology Planning&Evaluation)the Son Jiho Research Grant of Yonsei University(2023-22-0006:Taeyoung Park).
文摘Put options are known to be priced unusually high in the market,which we refer to as the overpriced put puzzle.This study proposes a quantum model(QM)that can explain such high put option prices as fair prices.Starting from a stochastic differential equation of stock returns,we convert the Fokker–Planck equation into the Schr鰀inger equation.To model the market force that always draws excess returns back to equilibrium,we specify a diffusion process corresponding to a QM with a delta potential.The results demonstrate that stock returns follow a Laplace distribution and exhibit power law in the tail.We then construct a closed-form solution for European put option pricing,determining that our model better explains the returns of the S&P 500 index and its corresponding put option prices than do geometric Brownian motion-based models.This study has significant implications for investors and risk managers,presenting a model that can potentially improve derivative pricing.Future studies can generalize the model assumptions by introducing asymmetric potential drawing back excess returns to equilibrium.
文摘From AR-enhanced picture books to eco-friendly smart toys,the items now filling children’s shopping carts are more than just products-they epitomize the transformation of consumption in the new era.
基金supported in part by Boeing Company and Nanjing University of Aeronautics and Astronautics(NUAA)through the Research on Decision Support Technology of Air Traffic Operation Management in Convective Weather under Project 2022-GT-129in part by the Postgraduate Research and Practice Innovation Program of NUAA(No.xcxjh20240709)。
文摘Addressing the issue that flight plans between Chinese city pairs typically rely on a single route,lacking alternative paths and posing challenges in responding to emergencies,this study employs the“quantile-inflection point method”to analyze specific deviation trajectories,determine deviation thresholds,and identify commonly used deviation paths.By combining multiple similarity metrics,including Euclidean distance,Hausdorff distance,and sector edit distance,with the density-based spatial clustering of applications with noise(DBSCAN)algorithm,the study clusters deviation trajectories to construct a multi-option trajectory set for city pairs.A case study of 23578 flight trajectories between the Guangzhou airport cluster and the Shanghai airport cluster demonstrates the effectiveness of the proposed framework.Experimental results show that sector edit distance achieves superior clustering performance compared to Euclidean and Hausdorff distances,with higher silhouette coefficients and lower Davies⁃Bouldin indices,ensuring better intra-cluster compactness and inter-cluster separation.Based on clustering results,19 representative trajectory options are identified,covering both nominal and deviation paths,which significantly enhance route diversity and reflect actual flight practices.This provides a practical basis for optimizing flight paths and scheduling,enhancing the flexibility of route selection for flights between city pairs.
