This paper proposes a new state space approach to adaptive fuzzy modeling under the dynamic environment, where Bayesian filtering sequentially learns the model parameters including model structures themselves as state variables. In particular, our approach specifies the state transitions as meanreversion processes, which intends to incorporate and extend the established state-of-art learning techniques as follows: First, the mean-reversion levels of model parameters are determined by applying some existing learning method to a training period. Next, filtering implementation over test data enables on-line estimation of the parameters, where the estimates are adaptively tuned for each new data arrival based on the obtained reliable learning result. In this work, we concretely design a Takagi-Sugeno- Kang fuzzy model for financial investment, whose parameters follow autoregressive processes with the mean-reversion levels decided by particle swarm optimization. Since there exist Monte Carlo simulation-based algorithms called particle filtering, our methodology is applicable to a quite general setting including non-linearity, which actually arises in our investment problem. Then, an out-of-sample numerical experiment with security price data successfully demonstrates its effectiveness.
{"title":"State Space Approach to Adaptive Fuzzy Modeling: Application to Financial Investment","authors":"M. Nakano, Akihiko Takahashi, Soichiro Takahashi","doi":"10.2139/ssrn.3055555","DOIUrl":"https://doi.org/10.2139/ssrn.3055555","url":null,"abstract":"This paper proposes a new state space approach to adaptive fuzzy modeling under the dynamic environment, where Bayesian filtering sequentially learns the model parameters including model structures themselves as state variables. In particular, our approach specifies the state transitions as meanreversion processes, which intends to incorporate and extend the established state-of-art learning techniques as follows: First, the mean-reversion levels of model parameters are determined by applying some existing learning method to a training period. Next, filtering implementation over test data enables on-line estimation of the parameters, where the estimates are adaptively tuned for each new data arrival based on the obtained reliable learning result. In this work, we concretely design a Takagi-Sugeno- Kang fuzzy model for financial investment, whose parameters follow autoregressive processes with the mean-reversion levels decided by particle swarm optimization. Since there exist Monte Carlo simulation-based algorithms called particle filtering, our methodology is applicable to a quite general setting including non-linearity, which actually arises in our investment problem. Then, an out-of-sample numerical experiment with security price data successfully demonstrates its effectiveness.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128713397","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}
The paper concerns small-area estimation in the heteroscedastic nested error regression (HNER) model which assumes that the within-area variances are different among areas. Although HNER is useful for analyzing data where the within-area variation changes from area to area, it is difficult to provide good estimates for the error variances because of small samples sizes for small-areas. To fix this difficulty, we suggest a random dispersion HNER model which assumes a prior distribution for the error variances. The resulting Bayes estimates of small area means provide stable shrinkage estimates even for small sample sizes. Next we propose an empirical Bayes procedure for estimating the small area means. For measuring uncertainty of the empirical Bayes estimators, we use the conditional and unconditional mean squared errors (MSE) and derive their second-order approximations. It is interesting to note that the difference between the two MSEs appears in the first-order terms while the difference appears in the second-order terms for classical normal linear mixed models. Second-order unbiased estimators of the two MSEs are given with an application to the posted land price data.
{"title":"Prediction in Heteroscedastic Nested Error Regression Models with Random Dispersions","authors":"T. Kubokawa, S. Sugasawa, M. Ghosh, S. Chaudhuri","doi":"10.5705/ss.202014.0070","DOIUrl":"https://doi.org/10.5705/ss.202014.0070","url":null,"abstract":"The paper concerns small-area estimation in the heteroscedastic nested error regression (HNER) model which assumes that the within-area variances are different among areas. Although HNER is useful for analyzing data where the within-area variation changes from area to area, it is difficult to provide good estimates for the error variances because of small samples sizes for small-areas. To fix this difficulty, we suggest a random dispersion HNER model which assumes a prior distribution for the error variances. The resulting Bayes estimates of small area means provide stable shrinkage estimates even for small sample sizes. Next we propose an empirical Bayes procedure for estimating the small area means. For measuring uncertainty of the empirical Bayes estimators, we use the conditional and unconditional mean squared errors (MSE) and derive their second-order approximations. It is interesting to note that the difference between the two MSEs appears in the first-order terms while the difference appears in the second-order terms for classical normal linear mixed models. Second-order unbiased estimators of the two MSEs are given with an application to the posted land price data.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128984965","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}
Pub Date : 2014-02-01DOI: 10.1628/001522114x685465
Toshihiro Ihori
a€€a€€ This study analyzes how commitment to a deficit ceiling can affect private agents' political efforts, as well as overall welfare, in a hard and a soft budget regime, using a two-period model simulating a present and a future generation and a government. In the hard budget regime, the government imposes the deficit ceiling before the present-generation's interest group decides the quantity of personal fiscal privileges. Since in the soft budget regime the government cannot commit itself to the deficit ceiling ex ante, the present generation exerts intense political efforts for personal fiscal privileges. We explore the interesting possibility that the soft budget regime leads to an overall welfare reduction for both generations, and hence, the commitment to a deficit ceiling benefits even rent-seeking private agents.
{"title":"Commitment, Deficit Ceiling, and Fiscal Privilege","authors":"Toshihiro Ihori","doi":"10.1628/001522114x685465","DOIUrl":"https://doi.org/10.1628/001522114x685465","url":null,"abstract":"a€€a€€ This study analyzes how commitment to a deficit ceiling can affect private agents' political efforts, as well as overall welfare, in a hard and a soft budget regime, using a two-period model simulating a present and a future generation and a government. In the hard budget regime, the government imposes the deficit ceiling before the present-generation's interest group decides the quantity of personal fiscal privileges. Since in the soft budget regime the government cannot commit itself to the deficit ceiling ex ante, the present generation exerts intense political efforts for personal fiscal privileges. We explore the interesting possibility that the soft budget regime leads to an overall welfare reduction for both generations, and hence, the commitment to a deficit ceiling benefits even rent-seeking private agents.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114507926","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}
Pub Date : 2013-06-17DOI: 10.1920/WP.CEM.2013.2713
Y. Arai, Hidehiko Ichimura
We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimisation problem is not well-defined when the sign of the product of the second derivatives of the underlying functions at the estimated points is positive. To address this problem, we theoretically define and construct estimators of the asymptotically first-order optimal (AFO) bandwidths which are well-defined regardless of the sign. They are based on objective functions which incorporate a second-order bias term. Our approach is general enough to cover estimation problems related to densities and regression functions at interior and boundary points. We provide a detailed treatment of the sharp regression discontinuity design. This article is accompanied by a web appendix in which we present omitted discussions, an algorithm to implement the proposed method for the sharp RSS and proofs for the main results.
{"title":"Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design","authors":"Y. Arai, Hidehiko Ichimura","doi":"10.1920/WP.CEM.2013.2713","DOIUrl":"https://doi.org/10.1920/WP.CEM.2013.2713","url":null,"abstract":"We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimisation problem is not well-defined when the sign of the product of the second derivatives of the underlying functions at the estimated points is positive. To address this problem, we theoretically define and construct estimators of the asymptotically first-order optimal (AFO) bandwidths which are well-defined regardless of the sign. They are based on objective functions which incorporate a second-order bias term. Our approach is general enough to cover estimation problems related to densities and regression functions at interior and boundary points. We provide a detailed treatment of the sharp regression discontinuity design. This article is accompanied by a web appendix in which we present omitted discussions, an algorithm to implement the proposed method for the sharp RSS and proofs for the main results.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132287796","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 smoothing spline is considered to propose a novel model for the time-varying quantile of the univariate time series using a state space approach. A correlation is further incorporated between the dependent variable and its one-step-ahead quantile. Using a Bayesian approach, an efficient Markov chain Monte Carlo algorithm is described where we use the multi-move sampler, which generates simultaneously latent time-varying quantiles. Numerical examples are provided to show its high sampling efficiency in comparison with the simple algorithm that generates one latent quantile at a time given other latent quantiles. Furthermore, using Japanese inflation rate data, an empirical analysis is provided with the model comparison.
{"title":"Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline","authors":"Yuta Kurose, Yasuhiro Omori","doi":"10.14490/JJSS.42.23","DOIUrl":"https://doi.org/10.14490/JJSS.42.23","url":null,"abstract":"A smoothing spline is considered to propose a novel model for the time-varying quantile of the univariate time series using a state space approach. A correlation is further incorporated between the dependent variable and its one-step-ahead quantile. Using a Bayesian approach, an efficient Markov chain Monte Carlo algorithm is described where we use the multi-move sampler, which generates simultaneously latent time-varying quantiles. Numerical examples are provided to show its high sampling efficiency in comparison with the simple algorithm that generates one latent quantile at a time given other latent quantiles. Furthermore, using Japanese inflation rate data, an empirical analysis is provided with the model comparison.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115356592","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}
Both Japan in the late 1980s and the U.S. in the mid-2000s experienced an unsustainable boom in real estate prices along with high stock market valuations, and when the bubble burst, many households and financial institutions found themselves in dire straits. One major lesson from this experience is that deleveraging attempts by individual economic agents in the aftermath of large financial imbalances can generate significant negative macroeconomic externalities. In Japan's case, a negative feedback loop developed among falling asset prices, financial instability, and stagnant economic activity. This negative feedback loop has sometimes been called "Japanization." Japan's deleveraging became serious because the negative feedback loop was not contained in its early stage of development. The Japanese government did not act promptly to recapitalize banks that were suffering from the erosion of their capital buffer due to their large holdings of stocks. As a result, Japan's banks only slowly recognized bad loans, while stopping lending to promising new projects. Slow, but protracted asset sales resulted in a long period of asse t price declines. Nonfinancial companies perceived the deterioration of their balance sheets as permanent and cut spending drastically. As Japan's economy stagnated, the total amount of bad loans turned out to be much larger than initially estimated. In contrast to Japan, U.S. policy authorities responded to the financial crisis since 2007 more quickly. Surely, they learned from Japan's experience. It is also important to recognize, however, that the market-based nature of the U.S. financial system, as compared to a Japanese financial sector. This paper also shows that a rapid response by a central bank in a situation of financial crisis and economic stagnation can be a better choice than allowing a process of Japanization to drag on for years. In a weak economy, interest rates are already very low and the zero lower bound on interest rates limits a central bank's ability to stimulate the economy further. Moreover , nonconventional monetary policy measures work by reducing risk premiums and spreads between long-term and short-term interest rates. However, when a long period of economic stagnation occurs, these spreads have a tendency to decline to low levels, which then limits the effectiveness of such measures.
{"title":"Deleveraging and Monetary Policy: Japan since the 1990s and the United States since 2007","authors":"K. Ueda","doi":"10.1257/JEP.26.3.177","DOIUrl":"https://doi.org/10.1257/JEP.26.3.177","url":null,"abstract":"Both Japan in the late 1980s and the U.S. in the mid-2000s experienced an unsustainable boom in real estate prices along with high stock market valuations, and when the bubble burst, many households and financial institutions found themselves in dire straits. One major lesson from this experience is that deleveraging attempts by individual economic agents in the aftermath of large financial imbalances can generate significant negative macroeconomic externalities. In Japan's case, a negative feedback loop developed among falling asset prices, financial instability, and stagnant economic activity. This negative feedback loop has sometimes been called \"Japanization.\" Japan's deleveraging became serious because the negative feedback loop was not contained in its early stage of development. The Japanese government did not act promptly to recapitalize banks that were suffering from the erosion of their capital buffer due to their large holdings of stocks. As a result, Japan's banks only slowly recognized bad loans, while stopping lending to promising new projects. Slow, but protracted asset sales resulted in a long period of asse t price declines. Nonfinancial companies perceived the deterioration of their balance sheets as permanent and cut spending drastically. As Japan's economy stagnated, the total amount of bad loans turned out to be much larger than initially estimated. In contrast to Japan, U.S. policy authorities responded to the financial crisis since 2007 more quickly. Surely, they learned from Japan's experience. It is also important to recognize, however, that the market-based nature of the U.S. financial system, as compared to a Japanese financial sector. This paper also shows that a rapid response by a central bank in a situation of financial crisis and economic stagnation can be a better choice than allowing a process of Japanization to drag on for years. In a weak economy, interest rates are already very low and the zero lower bound on interest rates limits a central bank's ability to stimulate the economy further. Moreover , nonconventional monetary policy measures work by reducing risk premiums and spreads between long-term and short-term interest rates. However, when a long period of economic stagnation occurs, these spreads have a tendency to decline to low levels, which then limits the effectiveness of such measures.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124569061","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 derive the empirical content of an instrumental variables model of sectoral choice with discrete outcomes. The partial identification results extend existing work on sharp bounds in binary choice threshold crossing models in allowing sector specific unobserved heterogeneity. Assumptions on selection include the simple, extended and generalized Roy models. The derived bounds are nonparametric intersection bounds and are simple enough to lend themselves to existing inference methods. Identification implications of exclusion restrictions are also derived. The derived bounds are applied to the analysis of the effect of Swan-Ganz catheterization and the robustness of previous findings to the introduction of procedure-specific unobserved heterogeneity is examined.
{"title":"Sharp Bounds in the Binary Roy Model","authors":"Marc Henry, Ismael Mourifié","doi":"10.2139/SSRN.1986497","DOIUrl":"https://doi.org/10.2139/SSRN.1986497","url":null,"abstract":"We derive the empirical content of an instrumental variables model of sectoral choice with discrete outcomes. The partial identification results extend existing work on sharp bounds in binary choice threshold crossing models in allowing sector specific unobserved heterogeneity. Assumptions on selection include the simple, extended and generalized Roy models. The derived bounds are nonparametric intersection bounds and are simple enough to lend themselves to existing inference methods. Identification implications of exclusion restrictions are also derived. The derived bounds are applied to the analysis of the effect of Swan-Ganz catheterization and the robustness of previous findings to the introduction of procedure-specific unobserved heterogeneity is examined.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131144171","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}
The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of uncertainty of EBLUP is the estimation of the mean squared error (MSE) and the confidence interval, which have been studied under the second-order accuracy in the literature. This paper provides the general analytical results for these two measures in the unified framework, namely, we derive the conditions on the general consistent estimators of the variance components to satisfy the third-order accuracy in the MSE estimation and the confidence interval in the general linear mixed normal models. Those conditions are shown to be satisfied by not only the maximum likelihood (ML) and restricted maximum likelihood (REML), but also the other estimators including the Prasad-Rao and Fay-Herriot estimators in specific models.
{"title":"On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy","authors":"T. Kubokawa","doi":"10.14490/JJSS.41.93","DOIUrl":"https://doi.org/10.14490/JJSS.41.93","url":null,"abstract":"The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of uncertainty of EBLUP is the estimation of the mean squared error (MSE) and the confidence interval, which have been studied under the second-order accuracy in the literature. This paper provides the general analytical results for these two measures in the unified framework, namely, we derive the conditions on the general consistent estimators of the variance components to satisfy the third-order accuracy in the MSE estimation and the confidence interval in the general linear mixed normal models. Those conditions are shown to be satisfied by not only the maximum likelihood (ML) and restricted maximum likelihood (REML), but also the other estimators including the Prasad-Rao and Fay-Herriot estimators in specific models.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129249906","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}
The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. A bench-mark estimator of the linear combination is an unbiased estimator, which is minimax, but inadmissible relative to the mean squared error. An interesting issue is what is a prior distribution which results in the generalized Bayes and minimax estimator. Although it seems plausible that the generalized Bayes estimator against the uniform prior over the restricted space should be minimax, it is shown to be not minimax when the number of the location parameters, k, is more than or equal to three, while it is minimax for k = 1. In the case of k = 2, a necessary and sufficient condition for the minimaxity is given, namely, the minimaxity depends on signs of coefficients of the linear combination. When the underlying distributions are normal, we can obtain a prior distribution which results in the generalized Bayes estimator satisfying minimaxity and admissibility. Finally, it is demonstrated that the estimation of ratio of normal variances converges to the estimation of difference of the normal positive means, which gives a motivation of the issue studied here.
{"title":"Minimax Estimation of Linear Combinations of Restricted Location Parameters","authors":"T. Kubokawa","doi":"10.1214/11-IMSCOLL802","DOIUrl":"https://doi.org/10.1214/11-IMSCOLL802","url":null,"abstract":"The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. A bench-mark estimator of the linear combination is an unbiased estimator, which is minimax, but inadmissible relative to the mean squared error. An interesting issue is what is a prior distribution which results in the generalized Bayes and minimax estimator. Although it seems plausible that the generalized Bayes estimator against the uniform prior over the restricted space should be minimax, it is shown to be not minimax when the number of the location parameters, k, is more than or equal to three, while it is minimax for k = 1. In the case of k = 2, a necessary and sufficient condition for the minimaxity is given, namely, the minimaxity depends on signs of coefficients of the linear combination. When the underlying distributions are normal, we can obtain a prior distribution which results in the generalized Bayes estimator satisfying minimaxity and admissibility. Finally, it is demonstrated that the estimation of ratio of normal variances converges to the estimation of difference of the normal positive means, which gives a motivation of the issue studied here.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114734185","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}
Pub Date : 2010-03-01DOI: 10.1142/S0219024910005796
K. Yamamoto, Seisho Sato, Akihiko Takahashi
This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al. [7]). The mathematical validity of the approximation is also proven. Then, numerical examples show that the instantaneous correlation between the asset value and the volatility state crucially affects the probability distribution and option prices for drawdown.
本文研究了随机波动环境下下跌的概率分布和期权定价问题。它们的解析近似公式是通过应用奇异摄动法推导出来的(Fouque et al.[7])。并证明了近似的数学有效性。然后，数值算例表明，资产价值与波动状态之间的瞬时相关性对回撤的概率分布和期权价格具有重要影响。
{"title":"Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment","authors":"K. Yamamoto, Seisho Sato, Akihiko Takahashi","doi":"10.1142/S0219024910005796","DOIUrl":"https://doi.org/10.1142/S0219024910005796","url":null,"abstract":"This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al. [7]). The mathematical validity of the approximation is also proven. Then, numerical examples show that the instantaneous correlation between the asset value and the volatility state crucially affects the probability distribution and option prices for drawdown.","PeriodicalId":345004,"journal":{"name":"CIRJE F-Series","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123796167","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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