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 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.
Venture capital investments are characterized by high input,high yield,and high risk.Due to the complexity of the market environment,stage-by-stage investment is becoming increasingly important.Traditional evaluation ...Venture capital investments are characterized by high input,high yield,and high risk.Due to the complexity of the market environment,stage-by-stage investment is becoming increasingly important.Traditional evaluation methods like comparison,proportion,maturity,internal rate of return,scenario analysis,decision trees,and net present value cannot fully consider the uncertainty and stage characteristics of the project.The fuzzy real options method addresses this by combining real option theory,fuzzy number theory,and composite option theory to provide a more accurate and objective evaluation of Public-Private Partnership(PPP)projects.It effectively considers the interaction of options and the ambiguity of project parameters,making it a valuable tool for project evaluation in the context of venture capital investment.展开更多
时序抽象作为分层强化学习的重要研究内容,允许分层强化学习智能体在不同的时间尺度上学习策略,可以有效解决深度强化学习难以处理的稀疏奖励问题。如何端到端地学习到优秀的时序抽象策略一直是分层强化学习研究面临的挑战。Option-Crit...时序抽象作为分层强化学习的重要研究内容,允许分层强化学习智能体在不同的时间尺度上学习策略,可以有效解决深度强化学习难以处理的稀疏奖励问题。如何端到端地学习到优秀的时序抽象策略一直是分层强化学习研究面临的挑战。Option-Critic(OC)框架在Option框架的基础上,通过策略梯度理论,可以有效解决此问题。然而,在策略学习过程中,OC框架会出现Option内部策略动作分布变得十分相似的退化问题。该退化问题影响了OC框架的实验性能,导致Option的可解释性变差。为了解决上述问题,引入互信息知识作为内部奖励,并提出基于互信息优化的Option-Critic算法(Option-Critic Algorithm with Mutual Information Optimization,MIOOC)。MIOOC算法结合了近端策略Option-Critic(Proximal Policy Option-Critic,PPOC)算法,可以保证下层策略的多样性。为了验证算法的有效性,把MIOOC算法和几种常见的强化学习方法在连续实验环境中进行对比实验。实验结果表明,MIOOC算法可以加快模型学习速度,实验性能更优,Option内部策略更有区分度。展开更多
In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space...In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.展开更多
Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view ...Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.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
There has been a growing trend toward fast food consumption in Saudi Arabia, especially among students. Although fast foods are high in calories, they are not nutritious. So, the frequent intake or consumption of fast...There has been a growing trend toward fast food consumption in Saudi Arabia, especially among students. Although fast foods are high in calories, they are not nutritious. So, the frequent intake or consumption of fast food is associated with many health problems, such as obesity, type 2 diabetes, and other cardiovascular diseases. As fast food consumption significantly increases, obesity and other health conditions become prevalent. This research aims to identify the intake and frequency of fast food meals among the students at the health campus (Jazan University) and its impact on their health. The researchers conducted a cross-sectional study at the health campus of Jazan University, Saudi Arabia, to investigate female college students’ consumption and frequency of fast-food meals. Fast food is a common activity among female students at The Health Campus in Jazan, with only 15% of students being overweight or obese. Studies have found that college students consume much fast food, particularly twice a week, and choose lower-fat options to limit their fat intake.展开更多
In the FinTech era,we contribute to the literature by studying the pricing of Bitcoin options,which is timely and important given that both Nasdaq and the CME Group have started to launch a variety of Bitcoin derivati...In the FinTech era,we contribute to the literature by studying the pricing of Bitcoin options,which is timely and important given that both Nasdaq and the CME Group have started to launch a variety of Bitcoin derivatives.We find pricing errors in the presence of market smiles in Bitcoin options,especially for short-maturity ones.Long-maturity options display more of a“smirk”than a smile.Additionally,the ARJI-EGARCH model provides a better overall fit for the pricing of Bitcoin options than the other ARJI-GARCH type models.We also demonstrate that the ARJI-GARCH model can provide more precise pricing of Bitcoin and its options than the SVCJ model in term of the goodness-of-fit in forecasting.Allowing for jumps is crucial for modeling Bitcoin options as we find evidence of time-varying jumps.Our empirical results demonstrate that the realized jump variation can describe the volatility behavior and capture the jump risk dynamics in Bitcoin and its options.展开更多
Modeling implied volatility(IV)is important for option pricing,hedging,and risk management.Previous studies of deterministic implied volatility functions(DIVFs)propose two parameters,moneyness and time to maturity,to ...Modeling implied volatility(IV)is important for option pricing,hedging,and risk management.Previous studies of deterministic implied volatility functions(DIVFs)propose two parameters,moneyness and time to maturity,to estimate implied volatility.Recent DIVF models have included factors such as a moving average ratio and relative bid-ask spread but fail to enhance modeling accuracy.The current study offers a generalized DIVF model by including a momentum indicator for the underlying asset using a relative strength index(RSI)covering multiple time resolutions as a factor,as momentum is often used by investors and speculators in their trading decisions,and in contrast to volatility,RSI can distinguish between bull and bear markets.To the best of our knowledge,prior studies have not included RSI as a predictive factor in modeling IV.Instead of using a simple linear regression as in previous studies,we use a machine learning regression algorithm,namely random forest,to model a nonlinear IV.Previous studies apply DVIF modeling to options on traditional financial assets,such as stock and foreign exchange markets.Here,we study options on the largest cryptocurrency,Bitcoin,which poses greater modeling challenges due to its extreme volatility and the fact that it is not as well studied as traditional financial assets.Recent Bitcoin option chain data were collected from a leading cryptocurrency option exchange over a four-month period for model development and validation.Our dataset includes short-maturity options with expiry in less than six days,as well as a full range of moneyness,both of which are often excluded in existing studies as prices for options with these characteristics are often highly volatile and pose challenges to model building.Our in-sample and out-sample results indicate that including our proposed momentum indicator significantly enhances the model’s accuracy in pricing options.The nonlinear machine learning random forest algorithm also performed better than a simple linear regression.Compared to prevailing option pricing models that employ stochastic variables,our DIVF model does not include stochastic factors but exhibits reasonably good performance.It is also easy to compute due to the availability of real-time RSIs.Our findings indicate our enhanced DIVF model offers significant improvements and may be an excellent alternative to existing option pricing models that are primarily stochastic in nature.展开更多
We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brown...We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brownian motion and stable processes.Further,we introduce the diagonal tempered stable model,which is parsimonious but allows for rich dependence between assets.Here,the number of parameters only grows linearly as the dimension increases,which makes it tractable in higher dimensions and avoids the so-called“curse of dimensionality.”As an illustration,we apply the model to price multi-asset options in two,three,and four dimensions.Detailed goodness-of-fit methods show that our model fits the data very well.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 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The research was funded by VSB-Technical University of Ostrava,the SGS Projects SP2022/58,SP2023/008.Huanyu Li,Ing.,Economic Faculty,VSB-TUO,Ostrava,Czech Republic。
文摘Venture capital investments are characterized by high input,high yield,and high risk.Due to the complexity of the market environment,stage-by-stage investment is becoming increasingly important.Traditional evaluation methods like comparison,proportion,maturity,internal rate of return,scenario analysis,decision trees,and net present value cannot fully consider the uncertainty and stage characteristics of the project.The fuzzy real options method addresses this by combining real option theory,fuzzy number theory,and composite option theory to provide a more accurate and objective evaluation of Public-Private Partnership(PPP)projects.It effectively considers the interaction of options and the ambiguity of project parameters,making it a valuable tool for project evaluation in the context of venture capital investment.
文摘时序抽象作为分层强化学习的重要研究内容,允许分层强化学习智能体在不同的时间尺度上学习策略,可以有效解决深度强化学习难以处理的稀疏奖励问题。如何端到端地学习到优秀的时序抽象策略一直是分层强化学习研究面临的挑战。Option-Critic(OC)框架在Option框架的基础上,通过策略梯度理论,可以有效解决此问题。然而,在策略学习过程中,OC框架会出现Option内部策略动作分布变得十分相似的退化问题。该退化问题影响了OC框架的实验性能,导致Option的可解释性变差。为了解决上述问题,引入互信息知识作为内部奖励,并提出基于互信息优化的Option-Critic算法(Option-Critic Algorithm with Mutual Information Optimization,MIOOC)。MIOOC算法结合了近端策略Option-Critic(Proximal Policy Option-Critic,PPOC)算法,可以保证下层策略的多样性。为了验证算法的有效性,把MIOOC算法和几种常见的强化学习方法在连续实验环境中进行对比实验。实验结果表明,MIOOC算法可以加快模型学习速度,实验性能更优,Option内部策略更有区分度。
基金supported by the Jiangsu University Philosophy and Social Science Research Project(Grant No.2019SJA1326).
文摘In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.
文摘Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.
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There has been a growing trend toward fast food consumption in Saudi Arabia, especially among students. Although fast foods are high in calories, they are not nutritious. So, the frequent intake or consumption of fast food is associated with many health problems, such as obesity, type 2 diabetes, and other cardiovascular diseases. As fast food consumption significantly increases, obesity and other health conditions become prevalent. This research aims to identify the intake and frequency of fast food meals among the students at the health campus (Jazan University) and its impact on their health. The researchers conducted a cross-sectional study at the health campus of Jazan University, Saudi Arabia, to investigate female college students’ consumption and frequency of fast-food meals. Fast food is a common activity among female students at The Health Campus in Jazan, with only 15% of students being overweight or obese. Studies have found that college students consume much fast food, particularly twice a week, and choose lower-fat options to limit their fat intake.
文摘In the FinTech era,we contribute to the literature by studying the pricing of Bitcoin options,which is timely and important given that both Nasdaq and the CME Group have started to launch a variety of Bitcoin derivatives.We find pricing errors in the presence of market smiles in Bitcoin options,especially for short-maturity ones.Long-maturity options display more of a“smirk”than a smile.Additionally,the ARJI-EGARCH model provides a better overall fit for the pricing of Bitcoin options than the other ARJI-GARCH type models.We also demonstrate that the ARJI-GARCH model can provide more precise pricing of Bitcoin and its options than the SVCJ model in term of the goodness-of-fit in forecasting.Allowing for jumps is crucial for modeling Bitcoin options as we find evidence of time-varying jumps.Our empirical results demonstrate that the realized jump variation can describe the volatility behavior and capture the jump risk dynamics in Bitcoin and its options.
文摘Modeling implied volatility(IV)is important for option pricing,hedging,and risk management.Previous studies of deterministic implied volatility functions(DIVFs)propose two parameters,moneyness and time to maturity,to estimate implied volatility.Recent DIVF models have included factors such as a moving average ratio and relative bid-ask spread but fail to enhance modeling accuracy.The current study offers a generalized DIVF model by including a momentum indicator for the underlying asset using a relative strength index(RSI)covering multiple time resolutions as a factor,as momentum is often used by investors and speculators in their trading decisions,and in contrast to volatility,RSI can distinguish between bull and bear markets.To the best of our knowledge,prior studies have not included RSI as a predictive factor in modeling IV.Instead of using a simple linear regression as in previous studies,we use a machine learning regression algorithm,namely random forest,to model a nonlinear IV.Previous studies apply DVIF modeling to options on traditional financial assets,such as stock and foreign exchange markets.Here,we study options on the largest cryptocurrency,Bitcoin,which poses greater modeling challenges due to its extreme volatility and the fact that it is not as well studied as traditional financial assets.Recent Bitcoin option chain data were collected from a leading cryptocurrency option exchange over a four-month period for model development and validation.Our dataset includes short-maturity options with expiry in less than six days,as well as a full range of moneyness,both of which are often excluded in existing studies as prices for options with these characteristics are often highly volatile and pose challenges to model building.Our in-sample and out-sample results indicate that including our proposed momentum indicator significantly enhances the model’s accuracy in pricing options.The nonlinear machine learning random forest algorithm also performed better than a simple linear regression.Compared to prevailing option pricing models that employ stochastic variables,our DIVF model does not include stochastic factors but exhibits reasonably good performance.It is also easy to compute due to the availability of real-time RSIs.Our findings indicate our enhanced DIVF model offers significant improvements and may be an excellent alternative to existing option pricing models that are primarily stochastic in nature.
文摘We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brownian motion and stable processes.Further,we introduce the diagonal tempered stable model,which is parsimonious but allows for rich dependence between assets.Here,the number of parameters only grows linearly as the dimension increases,which makes it tractable in higher dimensions and avoids the so-called“curse of dimensionality.”As an illustration,we apply the model to price multi-asset options in two,three,and four dimensions.Detailed goodness-of-fit methods show that our model fits the data very well.
