臺灣市場隱含波動率指標的探究：Taifex's VXO與展望理論

The property of market volatility index on Taiwan market: Taifex’s VXO and prospect theory

CBOE 推出的隱含波動率指標（VXO），被用來衡量當時市場風險感受，其與指數報酬往往形成如傾倒S 型的函數特性。檢視過去文獻，普遍以「槓桿效果」假說解釋二者的變動。然而近年大量文獻質疑「槓桿效果」假說不能完全解釋波動率與報酬變動的變動關係。據此，本文試圖以展望理論論述的投資人決策特性，補足「槓桿效果」的問題。同時，立基在行為學的解釋，隱含波動率指標的功能將包括提供集體投資人風險偏好的訊息。延此結論，本文以台股選擇權市場為標的，建立台股市場的隱含波動率指標(Taifex’s VXO)，其目的有二：其一即在建立具傳達投資人決策訊息的波動率指標。其二，藉由Taifex’s VXO 與指數報酬率的變動關係，分析本土投資人在不同的市場情境，所表現的風險偏好及決策行為特性。

The CBOE’s market volatility index (CBOE’s VXO) which is known for the “investor fear gauge” is used as a proxy in measuring the traders’ risk perception. Previous studies have looked at the relationship between CBOE’s VXO and return is asymmetric and non-linear, best described as a reclined downward sloping S-curve. The most common explanation ties the phenomenon to the hypothesis of “leverage effect”. However, it has been a puzzle in literatures due to numerous anomalies that call into question the “leverage effect” as explanation, it implies that the pattern of return and volatility can not be merely outright tied to “leverage effect”, but also needs to be explained by other causes. Since CBOE’s VXO is considered as the “fear gauge” in virtue of it has long recognized that it expresses the investors’ consensus view about futures market risk by literatures, and moreover, the “asymmetry” associated with the relationship between VXO and return, in which it suggests that panic strikes quickly but exuberance builds slowly, was posited as another form of loss aversion by the behavioral finance literature, we speculate the pattern of VXO-return relationship may arise from the behavioral peculiarities of options traders. Therefore, this article differs from past studies using “leverage effect” hypothesis but attempts to provide another potential explanation for VXO-return relationship by the traders’ behavior introduced in prospect theory. Base on the hypothesis of “prospect theory”, it is reasonable to speculate the properties of investors’ behavior will also reflects on VXO, including the unobserved risk preference. Thus, the volatility index is not only the estimator of market volatility, but also contains the information of the unobserved property of investors’ behavior. Recently, there is a growing literature on implied volatility indexes in the developed markets, however, there is no research has been conducted in the context of emerging markets. Taiwan derivative market has bloomed as an important emerging market, it does need to construct the local volatility index for Taiwan option market. Thus, the objective of this paper is threefold. First, it constructs an implied volatility index for fast growing Taiwan derivatives market, as mean of providing the complete information on investors’ behavior of Taiwan option market. Second, the properties of the constructed index is examined, it allows us to examine whether the traders’ risk preference in Taiwan market can be perceived by volatility index., which, in turn, the properties of investors’ behavior which are embedded in the constructed volatility index are examined accordingly. Finally, for further exploring the properties of investors’ behavior which embedded in the constructed volatility index, we futures examine the discrepancies in the investors’ behavior between Taiwan options market and the developed market. Three implied volatility indexes based on Taiwan index options market are constructed and discussed by this paper. One is IVTXO, which resembles CBOE’s VXO, another two indexes are IVC and IVP, which are constructed using only call and put options respectively by virtue of the information set associated with put and call options are probably different. By examining the properties of these three volatility indexes, we find that the patterns of IVP and IVTXO correlate with contemporaneous market conditions are closely to be a reclined S shape, however, only IVP fully corresponds to the idiosyncrasies of a volatility index as CBOE’s VXO. The finding suggests that IVP is not merely a volatility index of Taiwan market, but also an index which brings the information on the properties of investors’ behavior of Taiwan options market. Accordingly, the aggregated investors’ risk preference under risk can be perceived by IVP. Secondly, by further studying the relation between IVP and market return, there are at least two variations are found in the investors’ behavior between Taiwan options market and the developed market: (1)The investor of Taiwan market tends to hedge the risk perception by using options as the investors of the developed market, however, the tendency is relatively weaker for Taiwan investors; (2) Such hedge behavior associated with the Taiwan investors is only proved for put options contracts, and moreover, the tendency is only remarkable in the bear market.