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 paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and...The paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and interest rate derivatives contracted with their banks. Poland was the only EU country which did not precipitate into recession during the financial crisis beginning in 2008. However, the toxic fx and interest rate derivatives transmitted the shockwaves from global financial markets into Poland. Huge dimensions of losses resulted in conflicts between banks and their customers, who claimed just being cheated by the financial institutions. The article deeply researches into reasons for such developments on Polish fx over-the-counter derivatives market. As a case study, an authentic strategy has been presented. The contract was concluded between the construction company and one of the biggest commercial banks in Poland. Because the case study may be representative for many other cases, the analysis includes exact pricing of option strategy and therefore reveals inequality of the contract. The consequences of non-implementing the MiFID directive in the context of derivatives offering to non-financial customers were also touched in the paper.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
This paper deals with the issue of investment certificate formation in the financial market. Investment certificate is a type of structured products, the value of which is derived from the value of an underlying asset...This paper deals with the issue of investment certificate formation in the financial market. Investment certificate is a type of structured products, the value of which is derived from the value of an underlying asset. The underlying asset is usually a share in a company, a basket of shares, or an entire index, etc.. It can be stated that for every estimated development of an asset （growth, fall, and stagnation） or for every attitude to risks （conservative or aggressive investors）, there is a suitable kind of certificate. The main objective is to perform an analysis of the structured product--Austria/Germany Bond 3 and its guarantee certificate construction using digital-barrier options. The authors have found an alternative opportunity to the purchase of this certificate, i.e., investment in a bank deposit, together with a purchase of cash or nothing down and four-knock-out call options and a sale of cash or nothing down and four-knock-out put options. The authors prove that the alternative investment has the same profit profile as the certificate. The authors made this analysis with the objective to contribute to the intellectualization of investors.展开更多
The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes...The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes the American option value depends on the price change path of the underlying asset. And the ordinary American option pricing model underestimates the American option value. In order to fully reflect the long memory of the underlying asset return rates, we propose fractal American option pricing model, fractal Bermuda option pricing model, and a fractal combination of American option pricing model. Fractal American option value is greater than the ordinary American option value.展开更多
The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build ...The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build early exercise European option and early termination American option pricing models. Firstly, the authors reviewed the characteristics of American option and European option, then there was compares between them. Base on continuous-time American option pricing model, this research analyzed the value of these options.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The paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and interest rate derivatives contracted with their banks. Poland was the only EU country which did not precipitate into recession during the financial crisis beginning in 2008. However, the toxic fx and interest rate derivatives transmitted the shockwaves from global financial markets into Poland. Huge dimensions of losses resulted in conflicts between banks and their customers, who claimed just being cheated by the financial institutions. The article deeply researches into reasons for such developments on Polish fx over-the-counter derivatives market. As a case study, an authentic strategy has been presented. The contract was concluded between the construction company and one of the biggest commercial banks in Poland. Because the case study may be representative for many other cases, the analysis includes exact pricing of option strategy and therefore reveals inequality of the contract. The consequences of non-implementing the MiFID directive in the context of derivatives offering to non-financial customers were also touched in the paper.
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.
文摘This paper deals with the issue of investment certificate formation in the financial market. Investment certificate is a type of structured products, the value of which is derived from the value of an underlying asset. The underlying asset is usually a share in a company, a basket of shares, or an entire index, etc.. It can be stated that for every estimated development of an asset （growth, fall, and stagnation） or for every attitude to risks （conservative or aggressive investors）, there is a suitable kind of certificate. The main objective is to perform an analysis of the structured product--Austria/Germany Bond 3 and its guarantee certificate construction using digital-barrier options. The authors have found an alternative opportunity to the purchase of this certificate, i.e., investment in a bank deposit, together with a purchase of cash or nothing down and four-knock-out call options and a sale of cash or nothing down and four-knock-out put options. The authors prove that the alternative investment has the same profit profile as the certificate. The authors made this analysis with the objective to contribute to the intellectualization of investors.
文摘The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes the American option value depends on the price change path of the underlying asset. And the ordinary American option pricing model underestimates the American option value. In order to fully reflect the long memory of the underlying asset return rates, we propose fractal American option pricing model, fractal Bermuda option pricing model, and a fractal combination of American option pricing model. Fractal American option value is greater than the ordinary American option value.
文摘The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build early exercise European option and early termination American option pricing models. Firstly, the authors reviewed the characteristics of American option and European option, then there was compares between them. Base on continuous-time American option pricing model, this research analyzed the value of these options.
