An Empirical Analysis for Stock Liquidity in Option Pricing Model

[[abstract]]本研究以國內歐式股票選擇權為研究對象，以Black - Scholes選擇權評價模型及Krakovsky (1999)所提出的考慮股票流動性之選擇權評價模型來計算國內歐式股票選擇權之理論價格。Krakovsky (1999)模型沒有封閉解，本研究採用對數轉換之顯性有限差分法來求取其近似解。研究目的在於：1.以價格絕對誤差作為兩模型之評價誤差指標，分析Black - Scholes選擇權評價模型及Krakovsky (1999)模型對國內歐式股票選擇權之評價誤差。2.比較分析Krakovsky (1999)模型對國內歐式股票選擇權之評價能力是否較Black - Scholes選擇權評價模型為佳。 實證結果顯示：1.以Black - Scholes模型及Krakovsky (1999)模型計算之理論價皆明顯偏離國內歐式股票選擇權之市價。2. 整體而言，Krakovsky (1999)模型在評價國內歐式股票選擇權之評價能力優於Black - Scholes模型，對於價平及價外之國內股票選擇權、距到期日在120天內之國內股票選擇權，Krakovsky (1999)模型皆有顯著較Black - Scholes模型為佳之評價能力。[[abstract]]The objective of this paper is European stock option in Taiwan, using the pricing model of Black - Scholes (1973) and the option pricing model of Krakovsky (1999) that liquidity-adjusted Black-Scholes equation. Although the Krakovsky model does not the closed - form solution, we use the logarithmic explicit finite difference method searching the nearly solution. The goal of this paper is : 1.using the absolute pricing error to do the error of benchmark and analyzing the error between the Black - Scholes model and the Krakovsky model. 2.compling the Krakovsky model and the Black - Scholes model of European stock option in Taiwan which one can do the best pricing. The resultant of the demonstration is : 1. Both the Black — Scholes model and the Krakovsky model has obvious pricing error of European stock option in Taiwan. 2. The Krakovsky model do the best pricing than the Black - Scholes model in the at-the-money and out-the-money options, near-maturity options