從理性投機的觀點來解釋隱含波動率偏斜：台灣股市指數選擇權市場的校準

Explaining the Implied Volatility Skew from the Rational Speculation Perspective: Calibration on the Taiwan Stock Index Option Market

套利的限制與投資者心理—行為財務學的兩大基石—可以解釋台指選擇權市場的隱含波動率偏斜現象的成因。本文設計可描述造市者心理的投機模型，並採用當期貨市場出現套利受限時之即時資料，成功地校準出造市者對市場走勢有看法下之覺察的波動率（Perceived Volatility with a View），其具有與現貨市場波動率不對稱相似的型態。投機者在正向回饋交易者存在時的造市行為，是根據De Long等 （1990） 的不穩定理性投機論點，適用於噪音交易者充斥的市場。該論點有別於Black-Scholes模型的套利者之角色，其模型比較符合實務，且在波動率假設方面具有自我一致性。

The limits of arbitrage and investor psychology, the two cornerstones of behavioral finance, can explain the formation of implied volatility skew in the Taiwan stock index option market. Designing speculation models of the market maker’s psychology and adopting the real-time data that exhibit the limits of arbitrage in the futures market, this study successfully calibrates out the market maker’s “perceived volatility with a view,” showing a pattern similar to the volatility asymmetry in the spot market. The market-making of speculators in the prevalence of positive-feedback traders is based upon the argument of destabilizing rational speculation, pioneered by De Long et al. (1990), which is suitable for a market full of noise traders. Their argument disputes the role of arbitrageurs in the Black-Scholes Model. While our models, which are designed on the basis of this argument, reconcile with market practices, their calibrations on TXO market are self-consistent on the volatility assumption.