資產定價與流動性

Abstract

這篇論文是在假設基礎資產有流動性風險下探討選擇權的定價。在我們的模型裡，完全流動的基礎資產和不完全流動的基礎資產其價格是不同的，且在基礎資產有流動性風險下我們推導出流動性調整的選擇權理論價格。實證上，我們利用個股與個股選擇權的市場資料，從選擇權模型的定價表現和以選擇權觀點預測基礎資產價格分配函數的精準度這兩個面向，實證證明我們所發展的流動性調整選擇權定價模型優於傳統不考慮流動性風險的選擇權定價模型。 在論文的第一個部分，我們在假設基礎資產有流動性風險下推導出選擇權理論價格。我們利用流動性折扣因子來捕捉流動性對基礎資產價格的影響，且假設流動性折扣因子和市場流動性、股票對市場流動性的敏感程度有關。進一步，我們放鬆市場流動性為一隨機過程。利用個股與個股選擇權的資料，實證證明選擇權定價模型在納入基礎資產有流動性風險的調整下，其所推導出的理論價格會較非流動性調整選擇權定價模型所推導出的理論價格更接近市場價格。 在論文的第二部份，我們從選擇權的觀點推導出流動性調整的股價分配函數。我們比較在不同預測區間上的股價分配函數在股價的預測能力。實證結果證明流動性調整股價分配函數在股價的預測能力優於非流動性調整股價分配函數。

The purpose of this thesis is to investigate the pricing of options in which the underlying asset is not perfectly liquid. In this thesis, we show explicitly how the liquidity risk affects the prices of stock and we develop a liquidity-adjusted option pricing model. Empirically, we perform analysis of individual stocks and stock options to compare the performance of our proposed model with the traditional option pricing model in terms of pricing errors and the prediction quality of the densities for stock prices. In the first part of this thesis, we develop a liquidity-adjusted option pricing model in which the underlying asset is not perfectly liquid. The impact of liquidity risk on stock prices is modeled by a liquidity discount factor, which is related to the market liquidity and the stock’s sensitivity to market illiquidity. Specifically, we relax the market liquidity process, allowing it to be a stochastic framework. Empirically, we use individual stocks and stock options to show that our proposed model can effectively reduce pricing errors compared to the traditional option pricing model. In the second part of this thesis, we develop the liquidity-adjusted density of underlying asset prices from option prices. We compare the forecasting quality for one risk-neutral density and two real-world densities at different forecast horizons. Empirically, we show that our proposed densities are able to forecast future realizations of the underlying asset prices more accurately than the traditional densities.