論投機資產報酬：交易驅動之隨機走步模型

Abstract

本文立基於Clark, P. K. (1973)的經典股價波動模型，提出交易量(Q)即為運行時間(operational time)的設定。由此，可得知報酬(r)其實即為由交易量為步數所驅動的隨機走步(random walk)。此模型不但可以由直覺的兩個假設推導而出，更可由數個簡單的假設推導出許多符合實證結果的推論。實證方面，本文利用台灣股價資料，挑選最具代表性的150家公司，檢驗本模型所特有的線性股價變異數－交易量關係式，以及檢驗是否股價藉由√Q 調整趨向常態分佈。實證結果證實模型預測和數據的表現吻合。

This thesis proposes a model for speculative price that modifies the classic stochastic model of Clark, P. K. (1973) by simply adapting trading volume, Q, as the operational time. It suggests return is a random walk driven by trading volume. Not only can this model be derived from two intuitive assumptions, but also can several stylized facts of speculative price be derived from a few further assumptions that are supported by empirical evidences. Empirical evidence is examined for the most representative 150 companies in Taiwan stock market: A linear equation of trading volume and return conditional variance is confirmed to describe the real data well. After divided by √Q, return tends to be normally distributed.