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
The blockchain technology has been applied to wide areas.However,the open and transparent properties of the blockchains pose serious challenges to users’privacy.Among all the schemes for the privacy protection,the ze...The blockchain technology has been applied to wide areas.However,the open and transparent properties of the blockchains pose serious challenges to users’privacy.Among all the schemes for the privacy protection,the zero-knowledge proof algorithm conceals most of the private information in a transaction,while participants of the blockchain can validate this transaction without the private information.However,current schemes are only aimed at blockchains with the UTXO model,and only one type of assets circulates on these blockchains.Based on the zero-knowledge proof algorithm,this paper proposes a privacy protection scheme for blockchains that use the account and multi-asset model.We design the transaction structure,anonymous addresses and anonymous asset metadata,and also propose the methods of the asset transfer and double-spending detection.The zk-SNARKs algorithm is used to generate and to verify the zero-knowledge proof.And finally,we conduct the experiments to evaluate our scheme.展开更多
A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asse...A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.展开更多
Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boun...Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.展开更多
Based on the minimum loss probability criterion,this paper discusses the optimal strategy in multi-asset liquidation.First,we give the framework of the multi-asset liquidation problem and obtain the boundary condition...Based on the minimum loss probability criterion,this paper discusses the optimal strategy in multi-asset liquidation.First,we give the framework of the multi-asset liquidation problem and obtain the boundary conditions of the optimal liquidation strategy under the assumption of linear price impact functions and transform the multi-asset liquidation problem into the portfolio liquidation problem.On this basis,the asymptotic solution and numerical solution of the optimal liquidation strategy are obtained.Then,we simulate the trajectories of the optimal liquidation strategy and analyze the effects of parameters changes.展开更多
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.
基金supported by National Natural Science Foundation of China(61672499,61772502)Key Special Project of Beijing Municipal Science&Technology Commission(Z181100003218018)+1 种基金Natural Science Foundation of Inner Mongolia,Open Foundation of State key Laboratory of Networking and Switching Technology(Beijing University of Posts and Telecommunications,SKLNST-2016-2-09)SV-ICT Blockchain&DAPP Joint Lab
文摘The blockchain technology has been applied to wide areas.However,the open and transparent properties of the blockchains pose serious challenges to users’privacy.Among all the schemes for the privacy protection,the zero-knowledge proof algorithm conceals most of the private information in a transaction,while participants of the blockchain can validate this transaction without the private information.However,current schemes are only aimed at blockchains with the UTXO model,and only one type of assets circulates on these blockchains.Based on the zero-knowledge proof algorithm,this paper proposes a privacy protection scheme for blockchains that use the account and multi-asset model.We design the transaction structure,anonymous addresses and anonymous asset metadata,and also propose the methods of the asset transfer and double-spending detection.The zk-SNARKs algorithm is used to generate and to verify the zero-knowledge proof.And finally,we conduct the experiments to evaluate our scheme.
文摘A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.
文摘Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.
基金the National Natural Science Foundation of China(Grant No.71671017).
文摘Based on the minimum loss probability criterion,this paper discusses the optimal strategy in multi-asset liquidation.First,we give the framework of the multi-asset liquidation problem and obtain the boundary conditions of the optimal liquidation strategy under the assumption of linear price impact functions and transform the multi-asset liquidation problem into the portfolio liquidation problem.On this basis,the asymptotic solution and numerical solution of the optimal liquidation strategy are obtained.Then,we simulate the trajectories of the optimal liquidation strategy and analyze the effects of parameters changes.
