在財務領域的研究上大多定義異質信念為對資產未來的報酬率看法不一致。然而在真
實世界中，投資者對於資產價格的預測不僅僅只針對資產的投資報酬率，同時也會對
價格的波動率進行評估，因此對於波動率理應也存在著異質信念。本計畫有別於主流
文獻，將把研究目標定位在探討投資者對價格波動的異質信念對於資產評價的影響。
利用包含異質信念假設的連續時間模型，再配合完備市場的設定，我們企圖藉由此模
型推導出狀態-價格密度函數，再利用此密度函數去計算資產價格。另外我們也將討論
投資者對於波動看法的差異大小對於資產價格的影響。最後我們將利用投資者對波動
率的異質信念來解釋在選擇權市場中含隱波動率的微笑現象。
Most of the existing literature on belief heterogeneity is focused on
heterogeneous beliefs in an asset’s expected returns. However, in real world
situations, investors estimate not only an asset’s expected returns, but also its
volatility. In contrast to the mainstream literature in this area, the objective of
the current research is to study the influence of agents’ disagreement regarding
asset volatility on asset prices. Using a continuous-time model incorporating
heterogeneous beliefs in volatility and assuming that the market is complete, a
state-price density derived from this model can be used to compute asset prices.
Furthermore, how agent disagreement regarding volatility influences asset prices
will be discussed. Finally, we will try to explain that heterogeneous beliefs in
volatility can lead to a phenomenon that has become known as the smile effect
