Masaaki Fukasawa (Osaka University), Isao Ishida (Osaka University), Tsunehiro Ishihara (Hitotsubashi University), Shuichi Nagata (Kwansei Gakuin University), Teppei Ogihara (Osaka University), Masato Ubukata (Kushiro Public University of Economics),

Two Day Seminar (CSFI・大証寄附研究部門共催)

Topics in Volatility and Forecasting (Day 2)

Masaaki Fukasawa (Osaka University), Isao Ishida (Osaka University), Tsunehiro Ishihara (Hitotsubashi University), Shuichi Nagata (Kwansei Gakuin University), Teppei Ogihara (Osaka University), Masato Ubukata (Kushiro Public University of Economics),

8月23日（木）(Day 1)

http://www-csfi.sigmath.es.osaka-u.ac.jp/structure/activity/seminar.php?id=86

8月24日（金）(Day 2)

10:30-11:15 Masaaki Fukasawa (Osaka University)

Title: "Volatility Derivatives and Model-free Implied Leverage"

Abstract: We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black-Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular we show its simple relation to the Black-Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

11:20-12:05 Shuichi Nagata (Kwansei Gakuin University)

Title: "Volatility Forecast Comparison with Biased Proxy"

(A joint work with Kosuke Oya, Osaka University)

Abstract: The various loss functions are employed in the literature to evaluate the forecasting accuracy. However, the rankings of volatility forecasting models given by some loss functions can be misspecified by the error of a volatility proxy. Patton (2011) introduces a new class of loss functions which guarantee the consistency of the ranking (asymptotically) if the volatility proxy is unbiased. Recently, the common volatility proxy is realized variance (RV) in practice. However, it is natural to consider that RV does not satisfy the unbiasedness condition due to market microstructure noise. In this paper, we consider the consistency for the ranking of volatility forecasting when the volatility proxy is biased. We introduce a new notion for the robustness of loss functions to evaluate the effect of the biased volatility proxy on the loss functions and propose a method to choose the better loss function even if the volatility proxy is biased. We conduct a simulation study for access the performance of our method and it complements the theoretical result.

14:00-14:45 Masato Ubukata (Kushiro Public University of Economics)

Title: "The information content of model-free implied variance and jump risk"

Abstract: Many papers have examined the information content of implied volatility or variance from option prices in predicting future stock price variability. Also, there has been considerable research in understanding the potentially distinct roles of stochastic volatility and jumps in the underlying process. This paper focuses on the information content of implied large jump risk, which is measured by the difference between model-free implied variances with or without large jump component. We attempt to provide new empirical evidence on this issue in the framework of encompassing regressions.

14:50-15:35 Tsunehiro Ishihara (Hitotsubashi University)

Title: "Multivariate realized stochastic volatility model with leverage"

Abstract: A joint model of multivariate returns and realized measures of covariance is proposed. The model of returns is described by a multivariate stochastic volatility model with leverage. The matrix exponential transformation is used to keep the time varying covariance matrices positive definite. The measurement equation of the multivariate realized measure is formulated as a matrix log-linear form, which is a matrix-variate extension of Takahashi, Omori, and Watanabe (2009). A Bayesian estimation method using Markov chain Monte Carlo is discussed. The proposed model and estimation method are applied to stock return data.

15:35-16:00 coffee break

16:00-16:45 Isao Ishida (Osaka University)

Title: "On the Moving Quantile Effects in (Financial) Time Series"

(A joint work with Virmantas Kvedaras, Vilnius University)

Abstract: We introduce and investigate some properties of a class of nonlinear time series models with the moving order statistics present in the data generating process. This endogenizes the regime changes and allows for non-linear size effects e.g. where the impact of extreme and ordinary events substantially differs. We show by simulations that such effects can produce realizations looking as if the structural breaks were present in the data and having substantially flatter sample autocorrelation functions. Since the usual tests for omitted non-linearity have insufficient power against such type of non-linearity, a suitable test is proposed. Some empirical illustrations using stock market returns are presented.

16:50-17:35 Teppei Ogihara (Osaka University)

Title: "Parametric estimation for stochastic regression models from nonsynchronous observations"

Abstract: We study parametric estimation for stochastic regression models from nonsynchronous observations. The problem of nonsynchronous observations appears when estimating the covariance of security returns using high-frequency financial data. We construct a quasi-likelihood function of the model and study the asymptotic behavior of the maximum-likelihood type estimator and the Bayes type estimator when length of observation intervals goes to zero. For this purpose, we follow the approach of likelihood ratio random fields proposed by Ibragimov-Has'minski, and use the polynomial type large deviation inequalities introduced by Yoshida(2011).

Topics in Volatility and Forecasting (Day 2)

http://www-csfi.sigmath.es.osaka-u.ac.jp/structure/activity/seminar.php?id=86

8月24日（金）(Day 2)

10:30-11:15 Masaaki Fukasawa (Osaka University)

Title: "Volatility Derivatives and Model-free Implied Leverage"

Abstract: We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black-Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular we show its simple relation to the Black-Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

11:20-12:05 Shuichi Nagata (Kwansei Gakuin University)

Title: "Volatility Forecast Comparison with Biased Proxy"

(A joint work with Kosuke Oya, Osaka University)

Abstract: The various loss functions are employed in the literature to evaluate the forecasting accuracy. However, the rankings of volatility forecasting models given by some loss functions can be misspecified by the error of a volatility proxy. Patton (2011) introduces a new class of loss functions which guarantee the consistency of the ranking (asymptotically) if the volatility proxy is unbiased. Recently, the common volatility proxy is realized variance (RV) in practice. However, it is natural to consider that RV does not satisfy the unbiasedness condition due to market microstructure noise. In this paper, we consider the consistency for the ranking of volatility forecasting when the volatility proxy is biased. We introduce a new notion for the robustness of loss functions to evaluate the effect of the biased volatility proxy on the loss functions and propose a method to choose the better loss function even if the volatility proxy is biased. We conduct a simulation study for access the performance of our method and it complements the theoretical result.

14:00-14:45 Masato Ubukata (Kushiro Public University of Economics)

Title: "The information content of model-free implied variance and jump risk"

Abstract: Many papers have examined the information content of implied volatility or variance from option prices in predicting future stock price variability. Also, there has been considerable research in understanding the potentially distinct roles of stochastic volatility and jumps in the underlying process. This paper focuses on the information content of implied large jump risk, which is measured by the difference between model-free implied variances with or without large jump component. We attempt to provide new empirical evidence on this issue in the framework of encompassing regressions.

14:50-15:35 Tsunehiro Ishihara (Hitotsubashi University)

Title: "Multivariate realized stochastic volatility model with leverage"

Abstract: A joint model of multivariate returns and realized measures of covariance is proposed. The model of returns is described by a multivariate stochastic volatility model with leverage. The matrix exponential transformation is used to keep the time varying covariance matrices positive definite. The measurement equation of the multivariate realized measure is formulated as a matrix log-linear form, which is a matrix-variate extension of Takahashi, Omori, and Watanabe (2009). A Bayesian estimation method using Markov chain Monte Carlo is discussed. The proposed model and estimation method are applied to stock return data.

15:35-16:00 coffee break

16:00-16:45 Isao Ishida (Osaka University)

Title: "On the Moving Quantile Effects in (Financial) Time Series"

(A joint work with Virmantas Kvedaras, Vilnius University)

Abstract: We introduce and investigate some properties of a class of nonlinear time series models with the moving order statistics present in the data generating process. This endogenizes the regime changes and allows for non-linear size effects e.g. where the impact of extreme and ordinary events substantially differs. We show by simulations that such effects can produce realizations looking as if the structural breaks were present in the data and having substantially flatter sample autocorrelation functions. Since the usual tests for omitted non-linearity have insufficient power against such type of non-linearity, a suitable test is proposed. Some empirical illustrations using stock market returns are presented.

16:50-17:35 Teppei Ogihara (Osaka University)

Title: "Parametric estimation for stochastic regression models from nonsynchronous observations"

Abstract: We study parametric estimation for stochastic regression models from nonsynchronous observations. The problem of nonsynchronous observations appears when estimating the covariance of security returns using high-frequency financial data. We construct a quasi-likelihood function of the model and study the asymptotic behavior of the maximum-likelihood type estimator and the Bayes type estimator when length of observation intervals goes to zero. For this purpose, we follow the approach of likelihood ratio random fields proposed by Ibragimov-Has'minski, and use the polynomial type large deviation inequalities introduced by Yoshida(2011).

- 講 師：
- Masaaki Fukasawa (Osaka University), Isao Ishida (Osaka University), Tsunehiro Ishihara (Hitotsubashi University), Shuichi Nagata (Kwansei Gakuin University), Teppei Ogihara (Osaka University), Masato Ubukata (Kushiro Public University of Economics),
- テーマ：
- Topics in Volatility and Forecasting (Day 2)
- 日 時：
- 2012年08月24日（金）10:30-17:35
- 場 所：
- 大阪大学基礎工学研究科Ｉ棟 204
- 参加費：
- 無料
- アクセス：
- 会場までのアクセスは下記URLをご参照ください。

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