Taiwan Stock Index Research Articles

Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19

In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database.

Forecasting Volatility With Spot Index and Index Futures: Evidence From Taiwan

In this article, we use the volatility of the Taiwan Stock Index (TAIEX) and its futures in the encompassing regression model to respectively make asynchronous forecasts of realized volatility (RV) and implied volatility (IV). Initially, we discover that, to obtain a stationary RV with a stable, long memory parameter, the optimal sampling intervals for the intraday return were 9 and 30 minutes. We uncover that the spot volatility is more predictive of RV than the futures volatility. To forecast IV, the volatility of futures has more information content, helping to improve overall forecast performance. The result implies that the underlying asset of the TAIEX options (TXO) is approximately the index futures rather than the spot index, owing mainly to the demands for hedging and arbitrage from the TXO holders. Finally, we confirm the forecasting capability of our various models via extensive forecasting error and simulation exercises.

Forecasting Volatility in Taiwan with Encompassing Regression Models

Volatility forecasting is important both theoretically and in practice, varying by forecasting methods and financial markets. In this article, we explore this topic in the Taiwanese markets, using the encompassing regression models. We use the volatility of the Taiwan Stock Index (TAIEX) and its futures in the encompassing regression model to respectively make asynchronous forecasts of realized volatility (RV) and implied volatility (IV). Besides trading frequency, we find that transaction matching time is a key factor for obtaining steady RV values. Also, we find that the TAIEX index RV has a long memory. Moreover, we discover that, to obtain a stationary RV with a stable, long memory parameter, the optimal sampling intervals for the intraday return were nine (9) and thirty (30) minutes. In addition, we uncover that the spot volatility is more predictive of RV than the futures volatility. In the forecasting of IV, the volatility of futures has more information content, which can help improve overall forecast performance, especially when employing the ARFIMA+Jump model in the non-bear market and the ARFIMA+Jump/Leverage model in the bear market. The empirical result implies that the underlying asset of the TAIEX options (TXO) is approximately the index futures rather than the spot index, owing mainly to the demands for hedging and arbitrage from the TXO holders.

The Forecasting Efficiency of Monthly Stock Indices between Macroeconomic Factors and Technical Indicators by Using Augmented Genetic Algorithm and Artificial Neural Network Model

The purpose of this study is to compare the forecasting efficiency of stock indices between macroeconomics and technical analysis by using augmented Genetic Algorithm and Artificial Neural Network model. Monthly data of Taiwan stock index, electronic index, and financial index, from Jan. 2001 to Dec. 2019 are collected. Eight influential macroeconomic factors and seven commonly watched technical indicators are used as determinants. Three models are adopted for comparison. The models include the ARMA(p, q) model as the benchmark, GA_ANN with macroeconomic factors, and GA_ANN with technical indicators. The sliding window method with 24-, 30-, 36-, 42- and 48-month training base periods is simulated. Linear unit root tests of ADF, PP, and KPSS, and nonlinear unit root test of KSS are examined. Internal validity index of hit ratio and external validity indices of MAPE, HR, ARV and Theil U coefficients are compared. The empirical findings are summarized as follows. 1) The overall forecasting performance between MACRO and TECH models shows little difference. The electronic and financial stock indices have the out-of-sample hit ratios of 77.78% and 68.89%, respectively. Thus, these two stock indices may be suitable for making meaningful investment decisions. 2) The best training base observed from the market stock index is between 30 to 48 months. The best base observed from the electronic stock index is between 42 to 48 months. The best base observed from the financial stock index is between 42 to 48 months. Thus, the training base from 42 to 48 months exhibits better forecasting performance. 3) The optimal transformation parameter under ANN may range from 0.50 to 0.99 and may not be a constant parameter.

A Causal Time-Series Model Based on Multilayer Perceptron Regression for Forecasting Taiwan Stock Index

Stock forecasting technology is always a popular research topic because accurate forecasts allow profitable investments and social change. We postulate, based on past research, three major drawbacks for using time series in forecasting stock prices as follows: (1) a simple time-series model provides insufficient explanations for inner and external interactions of the stock market; (2) the variables of a time series behave in strict stationarity, but economic time-series are usually in a nonlinear or nonstationary state and (3) the forecasting factors of multivariable time-series are selected based on researcher’s knowledge, and such a method is a “subjective” way to construct a forecasting model. Therefore, this paper proposes a causal time-series model to select forecasting factors and builds a machine learning forecast model. The “Granger causality test” is utilized first in the proposed model to select the critical factors from technical indicators and market indexes; next, a “multilayer perceptron regression (MLPR)” is employed to construct a forecasting model. This paper collected financial data over a 13-year period (from 2003 to 2015) of the Taiwan stock index (TAIEX) as experimental datasets. Furthermore, the root mean square error (RMSE) was used as a performance indicator, and we use five forecasting models as comparison models. The results reveal that the proposed model outperforms the comparison models in forecasting accuracy and performs well for three key indicators. LAG1, S&P500 and DJIA, are critical factors in all 11 of our time sliding windows (T1–T11). We offer these results to investors to aid in their decision-making processes.

Downside jump risk and the levels of futures-cash basis

This study investigates the effect of downward market jump risk on the futures-cash basis in the Taiwan stock index futures market. Using the slope of the option implied volatility smirk as a proxy for the risk of large downward price moves, we find that market jump risk helps explain variations in basis. Increased downward jump risk decreases the basis. Indeed, the basis driven by downward jump risk is widened with decreasing time to expiration. After separating downward jump risk into unexpected and expected jump risks, we find that unexpected downward jump risk affects the basis, while no convincing evidence supports the expected downward jump risk effect. The downside jump risk effect is robust even when using the implied volatility skew and the return of a constructed jump risk-mimicking portfolio as proxies for downward jump risk and excluding the sample period from the 2008 financial crisis.

Regime-Switching Processes and Mean-Reverting Volatility Models in Value-at-Risk Estimation: Evidence from the Taiwan Stock Index

ABSTRACT This article develops a model that can accurately forecast the volatility of Taiwan stock returns and efficiently estimate value-at-risk (VaR). Because the volatility in the Taiwan stock market has been shown to die down and shift quickly, we find that the model able to outperform others is one that allows the parameters of the volatility models to switch between regimes and conditional volatility to revert quickly to near-normal levels following extremely volatile periods. Compared with nested models, this model has the best performance in terms of the statistical fit of in-sample data and out-of-sample volatility forecasts and VaR estimates.

Reasonable evaluation of VIX options for the Taiwan stock index

This study aims to reasonably evaluate VXO (volatility index option) prices on the Taiwan stock index using four popular pricing models, namely, Black-Scholes (BS), square root (SQR), log-normal Ornstein-Uhlenbeck (LOU), and GARCH models. Since VXOs have not been traded yet in Taiwan options market, we directly employ the physical probability measure to evaluate the VXOs. This study examined the Taiwan and CBOE VIX data from December 2006 to January 2018 and found that the estimated option prices generally appear in the descending order as GARCH > BS > SQR > LOU. That is, when VIX has heteroscedasticity, the BS model could undervalue the VXOs. Additionally, when VIX has no mean-reverting property, the SQR and LOU models could seriously undervalue the VXOs, especially for the long-term maturity options. While existing studies have not sufficiently evaluated the Taiwan VXOs, the results of this study can provide future reference for investors and securities companies when evaluating the Taiwan VXOs.

Testing the alternative two-state options pricing models: An empirical analysis on TXO

Considering the volatility in two states, the option pricing models involved constant volatility can be extended to two-state lognormal model (TLN), two-state constant-elasticity-variance model (TCEV) and two-state jump-diffusion model (TJD). Using Taiwan stock index, the parameters of transition between high- and low-volatility of the three two-state option pricing models are all estimated significant and then using TXO, we examine the three two-state models compared with the Black-Scholes model from two perspectives: strike prices and maturities in TXO. Overall, the option pricing performance of the four models in descending order are TLN, Black-Scholes, TCEV, and TJD in both call and put options while they have better pricing performance in put options than in call options. With the same strike price, the series of pricing errors across different maturities are nonstationary for the four models based on the unit root-test. However, with the different strike prices, the Johansen co-integration test of the different series of pricing errors are stationary and have finite variance. It appears that the spreads of pricing errors between different strikes are stable and mean reverse in the long run and the short run divergences from the equilibrium are vanished after all.

Cross-market information spillover and the performance of technical trading in the foreign exchange market

This study evaluates the effect of cross-market information spillover on the performance of popular variable-length moving averages (VMAs) for trading the daily exchange rates of New Taiwan Dollars to US Dollars (FXNTD/USD). Information incorporated in the Dow Jones Industrial Average (DJIA) and Taiwan Stock Index (TWSI) is introduced to study the effect. The results indicate that VMAs outperform the buy-and-hold strategy. Moreover, the information reflected in the DJIA and TWSI promotes the performance of VMAs. After correcting for data snooping bias, the DJIA is more informative than FXNTD/USD and the TWSI for VMAs.

Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work.

A novel method for forecasting time series based on fuzzy logic and visibility graph

Time series attracts much attention for its remarkable forecasting potential. This paper discusses how fuzzy logic improves accuracy when forecasting time series using visibility graph and presents a novel method to make more accurate predictions. In the proposed method, historical data is firstly converted into a visibility graph. Then, the strategy of link prediction is utilized to preliminarily forecast the future data. Eventually, the future data is revised based on fuzzy logic. To demonstrate the performance, the proposed method is applied to forecast Construction Cost Index, Taiwan Stock Index and student enrollments. The results show that fuzzy logic is able to improve the accuracy by designing appropriate fuzzy rules. In addition, through comparison, it is proved that our method has high flexibility and predictability. It is expected that our work will not only make contributions to the theoretical study of time series forecasting, but also be beneficial to practical areas such as economy and engineering by providing more accurate predictions.

Bayesian estimation of the Hurst parameter of fractional Brownian motion

ABSTRACTThe primary purpose of this study was to find Bayesian estimates for the Hurst dimension of a Fractional Brownian motion with a Beta prior when the process is observed at discrete times. Overestimation is observed though the overestimation is less severe as real H goes up. In addition, the estimated H decreases as Beta parameters go up given an Alpha value. In contrast, the estimated H increases as Alpha parameters go up given a Beta value. For the real-world data, the 2011 daily Taiwan stock index was used and the estimated Hurst index was 0.21.

Improving stock index forecasts by using a new weighted fuzzy-trend time series method

We propose using new weighted operators in fuzzy time series to forecast the future performance of stock market indices. Based on the chronological sequence of weights associated with the original fuzzy logical relationships, we define both chronological-order and trend-order weights, and incorporate our proposals for the ex-post forecast into the classical modeling approach of fuzzy time series. These modifications for the assignation of weights affect the forecasting process, because we use jumps as technical indicators to predict stock trends, and additionally, they provide a trapezoidal fuzzy number as a forecast of the future performance of the stock index value. Working with trapezoidal fuzzy numbers allows us to analyze both the expected value and the ambiguity of the future behavior of the stock index, using a possibilistic interval-valued mean approach. Therefore, using fuzzy logic more useful information is provided to the decision analyst, which should be appropriate in a financial context. We analyze the effectiveness of our approach with respect to other weighted fuzzy time series methods using trading data sets from the Taiwan Stock Index (TAIEX), the Japanese NIKKEI Index, the German Stock Index (DAX) and the Spanish Stock Index (IBEX35). The comparative results indicate the better accuracy of our procedure for point-wise one-step ahead forecasts.

Theories of Risk: Testing Investor Behaviour on the Taiwan Stock and Stock Index Futures Markets

Investor behavior towards risk lies at the heart of economic decision making in general and modern investment theory and practice in particular. This paper uses both the mean-variance (MV) criterion and stochastic dominance (SD) procedures to analyze the preferences for four of the most widely studied investor types in the Taiwan stock and stock index futures market. We find that risk averters (concave utility function) prefer spot to futures, whereas risk seekers (convex utility function) prefer futures to spot. Our findings also show that investors with S-shaped utility functions prefer spot (futures) to futures (spot) when markets move upward (downward). Finally, our results imply that investors with reverse S-shaped utility functions prefer futures (spot) to spot (futures) when markets move upward (downward). These results are robust with respect to sub-periods, spot returns including dividends and diversification. Although we do not check whether risk averters, risk seekers, and investors with S-shaped and reverse S-shaped utility functions actually exist in the market, we do show that their existence is plausible. The implications of our findings on market efficiency and the existence of arbitrage opportunities are also discussed in this study.

Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Mean reversion of stock price is an observed phenomenon in finance. It is similar to the concept of Newton's law of cooling. Three models of ordinary differential equation are derived from the concept and solved by dynamic integration. The models are applied to the daily closing price of Taiwan Stock Exchange Capitalisation Weighted Stock Index. Empirical study shows that the models have good fits and forecasts although errors appear during the dynamic forecasting process. The applicability of the models and future modification are also discussed.

Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Applications of linear ordinary differential equations and dynamic system to economics - an example of Taiwan stock index TAIEX

Stock index hedging using a trend and volatility regime-switching model involving hedging cost

In this study, the risk hedge between the Morgan Stanley Taiwan stock index (MSTI) and its underlying futures is analyzed regarding hedging cost under various hedge states using the trend and volatility involved regime-switching models compared with OLS and the naive method. The correlation between MSTI spot and futures is very high and the cointegration test between them is very significantly. The hedging result is evaluated using out-of-sample data and the realized variances and covariances, and is really satisfying in the subprime period or when both spot and future stay in a down state. In this stock index context, the risk aversion is determined to be 1. The optimal hedge ratio on average is around 0.878. The White test favors the regime-switching models in prediction. The trend and volatility-switching model performs particularly well in wealth increase.

Does options trading convey information on futures prices?

This paper studies the presence of informed trading in Taiwan stock index options (TXO) and analyzes the informational role of foreign institutions in incorporating information into Taiwan stock index futures (TX). We have found that only the option-induced part (OOI) of the total TX order imbalance can predict future TX prices, and the OOI calculated from open-buy TXO, defined by Ni et al. (2008), provides incremental predictability. This finding shows that the price predictability stems from the information flow resulting from option transactions rather than from liquidity pressure. We conclude further that option transactions from foreign institutions provide the most significant predictability, out-of-the-money option transactions in particular. These empirical results show that option transactions conducted by foreign institutions have played the primary role in conveying the information inherent in the TXO market to the TX market, foreign institutions being delta-informed traders. Retail investors, the major players in both the TXO and TX markets, have done almost nothing of significance with regard to TXO information transmission into the TX market, with the exception of some near-the-money and out-of-the-money options.

THEORIES OF RISK: TESTING INVESTOR BEHAVIOR ON THE TAIWAN STOCK AND STOCK INDEX FUTURES MARKETS

This article considers four utility functions—concave, convex, S‐shaped, and reverse S‐shaped—to analyze the behavior of different types of investors on the Taiwan stock index and its corresponding index futures. Using stochastic dominance (SD) rules, we show that the existence of all four investor types is plausible. Risk averters prefer spot to futures, whereas risk seekers prefer futures to spot. Investors with S‐shaped utility functions prefer spot (futures) to futures (spot) when markets move upward (downward). Investors with reverse S‐shaped utility functions prefer futures (spot) to spot (futures) when markets move upward (downward). We show that both spot and futures markets can exist when only risk averters are present, but futures can dominate spot only if there is some risk‐seeking behavior. These results are robust with respect to subperiods, spot returns including dividends, and diversification. (JEL C14, G12, G15)