The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to perform extrapolation outside the core region, choice of calibrating functional and selection of numerical optimization algorithms, volatility surface dynamics and asymptotics.
{"title":"Implied Volatility Surface: Construction Methodologies and Characteristics","authors":"Cristian Homescu","doi":"10.2139/ssrn.1882567","DOIUrl":"https://doi.org/10.2139/ssrn.1882567","url":null,"abstract":"The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to perform extrapolation outside the core region, choice of calibrating functional and selection of numerical optimization algorithms, volatility surface dynamics and asymptotics.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115864306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We first define and derive general properties of negative probabilities. We then show how negative probabilities can be applied to modeling financial options such as Caps and Floors. In trading practice, these options are typically valued in a Black-Scholes-Merton framework assuming a lognormal distribution for the underlying interest rate. However, in some cases, such as the 2008/2009 financial crisis, interest rates can get negative. Then the lognormal distribution is inapplicable. We show how negative probabilities associated with negative interest rates can be applied to value interest rate options. A model in VBA, which prices Caps and Floors with negative probabilities, is available upon request. A follow up paper will address bigger than unity probabilities in financial modeling.
{"title":"Negative Probabilities in Financial Modeling","authors":"G. Meissner, Dr. Mark Burgin","doi":"10.2139/ssrn.1773077","DOIUrl":"https://doi.org/10.2139/ssrn.1773077","url":null,"abstract":"We first define and derive general properties of negative probabilities. We then show how negative probabilities can be applied to modeling financial options such as Caps and Floors. In trading practice, these options are typically valued in a Black-Scholes-Merton framework assuming a lognormal distribution for the underlying interest rate. However, in some cases, such as the 2008/2009 financial crisis, interest rates can get negative. Then the lognormal distribution is inapplicable. We show how negative probabilities associated with negative interest rates can be applied to value interest rate options. A model in VBA, which prices Caps and Floors with negative probabilities, is available upon request. A follow up paper will address bigger than unity probabilities in financial modeling.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132344360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a model for optimal execution of the financial derivatives. We show that if rehedging of the underwriter of the derivative is considered, the optimal strategy is generally non-deterministic even for deterministic price impact functions. This approach can be utilized for optimal execution of the risky asset when the price impact functions are measurable with respect to the filtration generated by the risky asset.
{"title":"Optimal Execution of Derivatives","authors":"P. Novotný","doi":"10.2139/ssrn.1714094","DOIUrl":"https://doi.org/10.2139/ssrn.1714094","url":null,"abstract":"We present a model for optimal execution of the financial derivatives. We show that if rehedging of the underwriter of the derivative is considered, the optimal strategy is generally non-deterministic even for deterministic price impact functions. This approach can be utilized for optimal execution of the risky asset when the price impact functions are measurable with respect to the filtration generated by the risky asset.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127029721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we discuss the Malliavin differentiability of a particular class of Feller diffusions which we call $delta$-diffusions. This class is given by begin{equation*} dnu_t=kappa(theta-nu_t))dt eta nu_t^{delta}dmathbb W_t^2, deltain[frac{1}{2},1] end{equation*} and appears to be of relevance in Finance, in particular for interest and foreign-exchange models, as well as in the context of stochastic volatility models. We extend the result obtained in Alos and Ewald (2008) for $delta=frac{1}{2}$ and proof Malliavin differentiability for all $delta in [frac{1}{2},1]$.
本文讨论了一类特殊的Feller扩散的Malliavin可微性，我们称之为$delta$ -扩散。本课程由begin{equation*} dnu_t=kappa(theta-nu_t))dt eta nu_t^{delta}dmathbb W_t^2, deltain[frac{1}{2},1] end{equation*}提供，似乎与金融相关，特别是利息和外汇模型，以及随机波动率模型。我们推广了Alos和Ewald(2008)关于$delta=frac{1}{2}$的结果，并证明了所有$delta in [frac{1}{2},1]$的Malliavin可微性。
{"title":"Malliavin Differentiability of a Class of Feller-Diffusions with Relevance in Finance","authors":"C. Ewald, Yajun Xiao, Yang Zou, T. Siu","doi":"10.2139/ssrn.1425855","DOIUrl":"https://doi.org/10.2139/ssrn.1425855","url":null,"abstract":"In this paper we discuss the Malliavin differentiability of a particular class of Feller diffusions which we call $delta$-diffusions. This class is given by begin{equation*} dnu_t=kappa(theta-nu_t))dt eta nu_t^{delta}dmathbb W_t^2, deltain[frac{1}{2},1] end{equation*} and appears to be of relevance in Finance, in particular for interest and foreign-exchange models, as well as in the context of stochastic volatility models. We extend the result obtained in Alos and Ewald (2008) for $delta=frac{1}{2}$ and proof Malliavin differentiability for all $delta in [frac{1}{2},1]$.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128566445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A stock market model is presented that advances our understanding of the portfolio-consumption policy of investors and the behaviour of capital market statistics. The model's building blocks are the Samuelson-Merton model of portfolio-consumption policy, the Gordon-Sethi extension of that model to recognize bankruptcy, the Gordon dividend growth model for pricing a share, and the assumption that the system is closed. The last assumption makes price and expected return adjust to persuade investors to hold the outstanding shares and bonds. Analysis and simulation of the model reveal, among other things, that (1) the market is more stable and it performs better when investors have increasing relative risk aversion; and (2) the average infinite horizon return on a share falls below the average realized holding period return to a degree that varies with the volatility in the latter's return. Further advances in knowledge should follow from withdrawal of the simplifying assumptions that were employed to make clear the model's basic structure.
{"title":"A Stock Market Model","authors":"M. Gordon, S. Sethi","doi":"10.2139/ssrn.1293949","DOIUrl":"https://doi.org/10.2139/ssrn.1293949","url":null,"abstract":"A stock market model is presented that advances our understanding of the portfolio-consumption policy of investors and the behaviour of capital market statistics. The model's building blocks are the Samuelson-Merton model of portfolio-consumption policy, the Gordon-Sethi extension of that model to recognize bankruptcy, the Gordon dividend growth model for pricing a share, and the assumption that the system is closed. The last assumption makes price and expected return adjust to persuade investors to hold the outstanding shares and bonds. Analysis and simulation of the model reveal, among other things, that (1) the market is more stable and it performs better when investors have increasing relative risk aversion; and (2) the average infinite horizon return on a share falls below the average realized holding period return to a degree that varies with the volatility in the latter's return. Further advances in knowledge should follow from withdrawal of the simplifying assumptions that were employed to make clear the model's basic structure.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114734734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Purpose - The purpose of this paper is to investigate how quotes originating via electronic communication networks (ECN)s affect trading costs. Design/methodology/approach - In order to investigate the relations between trading costs and quotation venue, the bid-ask spread is decomposed into its theoretical cost components associated with adverse selection, inventory handling, and order processing. Findings - Stoll's adverse selection costs of ECN-originated quotes relate positively to effective spreads, while Lin Originality/value - The paper shows how trading costs relate to trading venue choice by decomposing the bid-ask spread.
{"title":"Electronic Communication Networks, Market Makers, and the Components of the Bid-Ask Spread","authors":"P.R. Daves, T. S. Strother, James W. Wansley","doi":"10.2139/ssrn.1024867","DOIUrl":"https://doi.org/10.2139/ssrn.1024867","url":null,"abstract":"Purpose - The purpose of this paper is to investigate how quotes originating via electronic communication networks (ECN)s affect trading costs. Design/methodology/approach - In order to investigate the relations between trading costs and quotation venue, the bid-ask spread is decomposed into its theoretical cost components associated with adverse selection, inventory handling, and order processing. Findings - Stoll's adverse selection costs of ECN-originated quotes relate positively to effective spreads, while Lin Originality/value - The paper shows how trading costs relate to trading venue choice by decomposing the bid-ask spread.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123755802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by economic and empirical arguments, we consider a company whose cash reservoir is affected by macroeconomic conditions. Specifically, we model the cash reservoir as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study three different cases: bounded dividend rates, unbounded dividend rates, and the case in which there are fixed costs and taxes associated to the dividend payments. These cases generate, respectively, problems of classical stochastic control with regime switching, singular stochastic control with regime switching,and stochastic impulse control with regime switching (a new problem in the stochastic control literature). We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. Our results shows, among other things, that the optimal dividend policy depends strongly on macroeconomic conditions.
{"title":"Classical, Singular, and Impulse Stochastic Control for the Optimal Dividend Policy when There is Regime Switching","authors":"Luz R. Sotomayor, A. Cadenillas","doi":"10.2139/ssrn.1139444","DOIUrl":"https://doi.org/10.2139/ssrn.1139444","url":null,"abstract":"Motivated by economic and empirical arguments, we consider a company whose cash reservoir is affected by macroeconomic conditions. Specifically, we model the cash reservoir as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study three different cases: bounded dividend rates, unbounded dividend rates, and the case in which there are fixed costs and taxes associated to the dividend payments. These cases generate, respectively, problems of classical stochastic control with regime switching, singular stochastic control with regime switching,and stochastic impulse control with regime switching (a new problem in the stochastic control literature). We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. Our results shows, among other things, that the optimal dividend policy depends strongly on macroeconomic conditions.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129446818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Going public is an important milestone for a firm. There are significant benefits and costs associated with the decision of being listed. On one hand the firm can raise the required capital for investment and firm growth through the IPO, make the firm more visible, transfer the risk to shareholders, and relax the borrowing constraints. It has significant implications for the product market competition too. The amount of cash generated through IPO if invested may also affect the future product market competition and the firm's profitability. On the other hand, going public is associated with significant amount of fixed costs and costs associated being under increased public scrutiny. The IPO process and the uncertainty associated are further complicated by the adverse selection problem associated with a firm taken public. The investors are asymmetrically informed about the future prospects of the firm relative to the management. The informational superiority of the firm leads to the standard lemons problem. The firm has to underprice the issue to give enough incentives to issuer to invest in the IPO. This is an indirect cost and lowers the IPO proceeds. The firm would therefore want to signal about its future prospects through its recent past performances. Hence going public decision and its implications are inherently dynamic in nature. The (management of the) firm thus wants to time the IPO decision well. Many of the associated costs and benefits are hidden. In this paper we formulate a dynamic programming based structural model of the decision to go public and estimate these hidden parameters using data from Indian IPOs. We model the going public decision as an optimal stopping time problem for a firm in a dynamic setting. Each period the management of the utility maximizing firm decides whether to list the firm or not. The source of management's consumption is the profit it generates through its profit maximizing investment decisions for the firm. Each period the management decides (a discrete choice) whether to take the firm public or not. Given its going public decision it chooses the level of investment (continuous choice) and consumes the rest. If the firm decides to go public, the firm makes the static (continuous choice) decision of how much of the firm to sell (dilution) and how much of the IPO proceed to reinvest. Although these decisions are static, its implications are dynamic in nature. The dilution decision is an outcome of the trade off between the IPO proceeds and the claim of the management on the future profits and private benefits of control of the firm. The IPO proceed reinvest decision is an equilibrium outcome of the trade off between the cash out prospect and future profitability improvement (hence improved managerial income) of the firm. We formulate a dynamic programming model and characterize the equilibrium. We outline a dynamic programming based structural estimation procedure to estimate the model parameters. The mod
{"title":"IPO as an Optimal Stopping Time: A Structural Estimation","authors":"Sudip Gupta, John Rust","doi":"10.2139/SSRN.1107924","DOIUrl":"https://doi.org/10.2139/SSRN.1107924","url":null,"abstract":"Going public is an important milestone for a firm. There are significant benefits and costs associated with the decision of being listed. On one hand the firm can raise the required capital for investment and firm growth through the IPO, make the firm more visible, transfer the risk to shareholders, and relax the borrowing constraints. It has significant implications for the product market competition too. The amount of cash generated through IPO if invested may also affect the future product market competition and the firm's profitability. On the other hand, going public is associated with significant amount of fixed costs and costs associated being under increased public scrutiny. The IPO process and the uncertainty associated are further complicated by the adverse selection problem associated with a firm taken public. The investors are asymmetrically informed about the future prospects of the firm relative to the management. The informational superiority of the firm leads to the standard lemons problem. The firm has to underprice the issue to give enough incentives to issuer to invest in the IPO. This is an indirect cost and lowers the IPO proceeds. The firm would therefore want to signal about its future prospects through its recent past performances. Hence going public decision and its implications are inherently dynamic in nature. The (management of the) firm thus wants to time the IPO decision well. Many of the associated costs and benefits are hidden. In this paper we formulate a dynamic programming based structural model of the decision to go public and estimate these hidden parameters using data from Indian IPOs. We model the going public decision as an optimal stopping time problem for a firm in a dynamic setting. Each period the management of the utility maximizing firm decides whether to list the firm or not. The source of management's consumption is the profit it generates through its profit maximizing investment decisions for the firm. Each period the management decides (a discrete choice) whether to take the firm public or not. Given its going public decision it chooses the level of investment (continuous choice) and consumes the rest. If the firm decides to go public, the firm makes the static (continuous choice) decision of how much of the firm to sell (dilution) and how much of the IPO proceed to reinvest. Although these decisions are static, its implications are dynamic in nature. The dilution decision is an outcome of the trade off between the IPO proceeds and the claim of the management on the future profits and private benefits of control of the firm. The IPO proceed reinvest decision is an equilibrium outcome of the trade off between the cash out prospect and future profitability improvement (hence improved managerial income) of the firm. We formulate a dynamic programming model and characterize the equilibrium. We outline a dynamic programming based structural estimation procedure to estimate the model parameters. The mod","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"488 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133321617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes a dynamic multivariate jump driven model in a credit setting. We set up a dynamic Levy model, more precisely a Multivariate Variance Gamma (VG) model, for a series of correlated spreads. The parameters of the model come from a two step calibration procedure. First, a joint calibration on swaptions on the spreads is performed and second, a correlation matching procedure is applied. For the first calibration step, we make use of equity-like pricing formulas for payer and receiver swaptions, based on the characteristic function and the Fast Fourier Transform (FFT) method. In the second calibration step, we fix the correlation in the model to match the prescribed (in casu historically observed) correlation. This can be done fast since a closed form expression is readily available. The resulting jump driven dynamic model generates correlated spreads very fast. This model can be used to price a whole range of exotic structures. We illustrate this by pricing the currently popular credit Constant Proportion Portfolio Insurance (CPPI) structures. Because of the built in jump dynamics a better assessment of gap risk is possible.
{"title":"Let's Jump Together - Pricing of Credit Derivatives: From Index Swaptions to CPPIs","authors":"João Garcia, S. Goossens, W. Schoutens","doi":"10.2139/ssrn.1358704","DOIUrl":"https://doi.org/10.2139/ssrn.1358704","url":null,"abstract":"This paper describes a dynamic multivariate jump driven model in a credit setting. We set up a dynamic Levy model, more precisely a Multivariate Variance Gamma (VG) model, for a series of correlated spreads. The parameters of the model come from a two step calibration procedure. First, a joint calibration on swaptions on the spreads is performed and second, a correlation matching procedure is applied. For the first calibration step, we make use of equity-like pricing formulas for payer and receiver swaptions, based on the characteristic function and the Fast Fourier Transform (FFT) method. In the second calibration step, we fix the correlation in the model to match the prescribed (in casu historically observed) correlation. This can be done fast since a closed form expression is readily available. The resulting jump driven dynamic model generates correlated spreads very fast. This model can be used to price a whole range of exotic structures. We illustrate this by pricing the currently popular credit Constant Proportion Portfolio Insurance (CPPI) structures. Because of the built in jump dynamics a better assessment of gap risk is possible.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125769336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Classical models of inflation, utilising the transactions-based demand for money, predict that monetary policy will be ineffective in changing real variables. In response to this, the New Keynesian sticky-price models assume price-rigidity in order to address the possibility for the existence of real effects of monetary policy. At the same time, both major theories have difficulty in explaining persistency in the money demand of households in the absence of uncertainty. We develop a flexible price model with endogenous transactions-costs driven demand for money that captures the possibility for real effects of monetary policy and accounts for the persistency of money demand. In our model, persistency is derived from transactions technology that assumes the existence of learning-by-doing effects in shopping costs. We proceed to compare the model with the standard monetary model of inflation.
{"title":"Monetary Theory of Inflation and the LBD in Transactions Technology","authors":"Constantin Gurdgiev","doi":"10.2139/ssrn.1105025","DOIUrl":"https://doi.org/10.2139/ssrn.1105025","url":null,"abstract":"Classical models of inflation, utilising the transactions-based demand for money, predict that monetary policy will be ineffective in changing real variables. In response to this, the New Keynesian sticky-price models assume price-rigidity in order to address the possibility for the existence of real effects of monetary policy. At the same time, both major theories have difficulty in explaining persistency in the money demand of households in the absence of uncertainty. We develop a flexible price model with endogenous transactions-costs driven demand for money that captures the possibility for real effects of monetary policy and accounts for the persistency of money demand. In our model, persistency is derived from transactions technology that assumes the existence of learning-by-doing effects in shopping costs. We proceed to compare the model with the standard monetary model of inflation.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123456821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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