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
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
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
The polynomial spline model, which belongs to the static term structure model of interest rates, is studied. Every cash flow of the project is discounted relatively accurately by obtaining the discount rate from the s...The polynomial spline model, which belongs to the static term structure model of interest rates, is studied. Every cash flow of the project is discounted relatively accurately by obtaining the discount rate from the static term structure model of interest rates. A simple basic model, which belongs to the dynamic term structure model, is studied, and the option pricing formula under changing risk-free rates is obtained by bringing it into the option pricing formula. Both dynamic and static term structure models are estimated by the use of the data of buy-back rates and the Shanghai Stock Exchange, and an example is given to compare the differences between the traditional method and the method under the changes in the interest rates and the discount rates.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.
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.
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.
基金The Achievements of Young Fund Project of Humanitiesand Social Science of Ministry of Education(No.07JC790028)the NationalNatural Science Foundation of China (No.70671025).
文摘The polynomial spline model, which belongs to the static term structure model of interest rates, is studied. Every cash flow of the project is discounted relatively accurately by obtaining the discount rate from the static term structure model of interest rates. A simple basic model, which belongs to the dynamic term structure model, is studied, and the option pricing formula under changing risk-free rates is obtained by bringing it into the option pricing formula. Both dynamic and static term structure models are estimated by the use of the data of buy-back rates and the Shanghai Stock Exchange, and an example is given to compare the differences between the traditional method and the method under the changes in the interest rates and the discount rates.
